diff --git a/TATA54/TENTOR/tenta-TATA54-20240822-losning.log b/TATA54/TENTOR/tenta-TATA54-20240822-losning.log
index a8b5678cbff98852c6694d0ef62c9d30b24ba75d..e9be7f5ee43fd9a40629597210eda39e41fce46f 100644
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diff --git a/TATA54/TENTOR/tenta-TATA54-20240822-losning.pdf b/TATA54/TENTOR/tenta-TATA54-20240822-losning.pdf
index 04a1c401d7ffbe6420aa5acb168628761eef8a87..34f831aaf168f2a7b0660a02384565b351b6565c 100644
Binary files a/TATA54/TENTOR/tenta-TATA54-20240822-losning.pdf and b/TATA54/TENTOR/tenta-TATA54-20240822-losning.pdf differ
diff --git a/TATA54/TENTOR/tenta-TATA54-20240822-losning.tex b/TATA54/TENTOR/tenta-TATA54-20240822-losning.tex
index e0141a6216c829abdcd3adbed3f1d2f5c8cb8106..0c1a8b6a90798b77ca1b94f48d484fac3ba0e282 100644
--- a/TATA54/TENTOR/tenta-TATA54-20240822-losning.tex
+++ b/TATA54/TENTOR/tenta-TATA54-20240822-losning.tex
@@ -1,6 +1,6 @@
 \documentclass[10pt,a4paper]{article}
-\usepackage{times}
-\usepackage{euler}
+%\usepackage{times}
+%\usepackage{euler}
 \usepackage{a4wide}
 \usepackage{enumerate}
 \usepackage{amsmath,amssymb,amsthm}
@@ -65,15 +65,17 @@ Båda dessa avbildningar respekterar rationalitet, så de rationella punkterna p
 \(x^2 \equiv 187 \mod 23\)?
 
 \soln 23 är ett primtal, och
-\(\legendre{187}{23} = \legendre{3}{23} = - \legendre{23}{3} = - \legendre{2}{3}
-=1\). Alltså har 187 precis 2 kvadratrötter modulo 23.
+\(\legendre{187}{23} = \legendre{3}{23}
+= - \legendre{23}{3} = - \legendre{2}{3}=1\).
+Alltså har 187 precis 2 kvadratrötter modulo 23 (dessa är \(x \equiv \pm 7 \mod 23\)).
 
 \item
   Hur många  lösningar har kongruensen
   \(x^2 \equiv 23 \mod 187\)?
 
   \soln \(187=11*17\) och
-  \(\legendre{23}{17}=\legendre{6}{17} = \legendre{2}{17} \legendre{3}{17}\)
+  \(\legendre{23}{17}=\legendre{6}{17} = \legendre{2}{17} \legendre{3}{17} = -1\),
+  så lösningar saknas modulo 17. Alltså finns det inga lösningar modulo 187.
 
  \item
    LÃ¥t \(r=117/119\). Hitta positiva heltal \(a,b\) med \(b < 119\)
@@ -84,6 +86,11 @@ Båda dessa avbildningar respekterar rationalitet, så de rationella punkterna p
    för alla
    positiva heltal \(c,d\) med \(d < 119\).
 
+   \soln Kedjebråksutvecklingen är \(117/118 = [0; 1,58,2]\)
+   med konvergenter \(0,1,58/59, 117/118\). Enligt sats i boken kan ingen rationell approximation
+   till \(117/118\) slå \(58/59\) utan att ha större nämnare. (Samma sak gäller i och för sig
+   också för den triviala
+   approximationen \(1/1\)).
 
 \item
   LÃ¥t \(\tau(n)\) beteckna antalet positiva delare till det positiva heltalet \(n\),
@@ -95,7 +102,14 @@ Båda dessa avbildningar respekterar rationalitet, så de rationella punkterna p
      \]
      för alla positiva heltal \(n\)? Ge bevis eller motexempel.
 
-     %https://math.stackexchange.com/questions/1749204/sum-of-number-of-divisors-function-equals-sum-j-1n-lfloor-n-j-rfloor
+
+     \soln
+    \begin{align*}
+      \sum_{k=1}^n \tau(k) &= \sum_{k=1}^n \sum_{1 \le d \le k, \,\divides{d}{k}} 1 \\
+        & = \sum_{d=1}^n \sum_{1 \le k \le n,\, k \in d\Z} 1 \\
+     & =  \sum_{1 \le d \le n} \lfloor n/d \rfloor
+   \end{align*}
+   %https://math.stackexchange.com/questions/1749204/sum-of-number-of-divisors-function-equals-sum-j-1n-lfloor-n-j-rfloor
 \end{enumerate}
 
 
diff --git a/TATA54/TENTOR/tenta-TATA54-20240822-skiss.org b/TATA54/TENTOR/tenta-TATA54-20240822-skiss.org
index e2c2e47025de67e2ad892f99a79e231669c05c2d..922d77621f673301ce4834871afbf2d5031851ca 100644
--- a/TATA54/TENTOR/tenta-TATA54-20240822-skiss.org
+++ b/TATA54/TENTOR/tenta-TATA54-20240822-skiss.org
@@ -198,6 +198,9 @@ f = x^2 -23
 f.roots(Integers(187),multiplicities=False)
 f.roots(Integers(11),multiplicities=False)
 f.roots(Integers(17),multiplicities=False)
+
+g = x^2 -187
+g.roots(Integers(23),multiplicities=False)
 #+end_src
 
 #+RESULTS:
@@ -206,6 +209,7 @@ f.roots(Integers(17),multiplicities=False)
 : []
 : [10, 1]
 : []
+: [16, 7]
 
 ** U7
 #+begin_src latex
@@ -228,6 +232,7 @@ r=p/q
 cf = continued_fraction(r)
 cf
 best = cf.convergent(2)
+best
 fel = abs(p/q - best)
 "kedjebråkapprox fel", fel
 
@@ -242,6 +247,7 @@ for j in range(2,q):
 #+RESULTS:
 #+begin_example
 [0; 1, 58, 2]
+58/59
 ('kedjebråkapprox fel', 1/7021)
 2 0.483193277310924 0.0168067226890756 0.000142429853297251
 3 0.316526610644258 0.0168067226890756 0.000142429853297251
diff --git a/homepage/exams/2024/tenta-TATA54-20240822-losning.pdf b/homepage/exams/2024/tenta-TATA54-20240822-losning.pdf
new file mode 100644
index 0000000000000000000000000000000000000000..34f831aaf168f2a7b0660a02384565b351b6565c
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diff --git a/homepage/exams/2024/tenta-TATA54-20240822.pdf b/homepage/exams/2024/tenta-TATA54-20240822.pdf
new file mode 100644
index 0000000000000000000000000000000000000000..d839e73d319edc0de99e0682c720582432af21ae
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diff --git a/homepage/index.org b/homepage/index.org
index 7b96fe3df032b9944f428db480ab90735ebc6666..983a2671c24151b7a05ca433b2ce203a4e23a2eb 100644
--- a/homepage/index.org
+++ b/homepage/index.org
@@ -413,6 +413,7 @@ De svenska versionerna är nyare. Några av föreläsningarna tar två tillfäll
 
 |      Datum | Examinator      | Tentamen                  | Lösningar                   |
 |------------+-----------------+---------------------------+-----------------------------|
+| 2024-08-22  | Jan Snellman    | [[file:exams/2024/tenta-TATA54-20240822.pdf][TATA5420240822]]            | [[file:exams/2024/tenta-TATA54-20240822-losning.pdf][TATA5420240822losn]]          |
 | 2024-06-01 | Jan Snellman    | [[file:exams/2024/tenta-TATA54-20240601.pdf][TATA5420240601]]            | [[file:exams/2024/tenta-TATA54-20240601-losning.pdf][TATA5420240601losn]]          |
 | 2023-08-17 | Jan Snellman    | [[file:exams/2023/tenta-TATA54-20230817.pdf][TATA5420230817]]            | [[file:exams/2023/tenta-TATA54-20230817soln.pdf][TATA5420230817soln]]          |
 | 2023-06-03 | Jan Snellman    | [[file:exams/2023/tenta-TATA54-20230603.pdf][TATA5420230603]]            | [[file:exams/2023/tenta-TATA54-20230603losn.pdf][TATA5420230603losn]]          |
diff --git a/homepage/sitemap.org b/homepage/sitemap.org
index 6e844ccd2d633f1398c3404a71d30020fba6c1a3..89f01736841522bb59ce8f53b542657d9adff995 100644
--- a/homepage/sitemap.org
+++ b/homepage/sitemap.org
@@ -1,15 +1,15 @@
 #+TITLE: Kurshemsida
 
-- [[file:newlectures/newlecture.org][Föreläsningar i Talteori]]
-- [[file:newlectures/new-lect-0.org][Talteori översiktsföreläsning]]
+- [[file:index.org][TATA54 Talteori]]
+- [[file:senaste-nytt.org][senaste-nytt]]
+- [[file:lectures/Henselfaktorisering.org][Henselfaktorisering]]
 - [[file:labs/lecture5.org][lecture5]]
 - [[file:labs/lecture4.org][lecture4]]
 - [[file:labs/lecture3.org][lecture3]]
 - [[file:labs/lecture2.org][lecture2]]
 - [[file:labs/lecture1.org][lecture1]]
 - [[file:labs/lecture0.org][lecture0]]
-- [[file:index.org][TATA54 Talteori]]
-- [[file:senaste-nytt.org][senaste-nytt]]
 - [[file:labs/kedjebraklab.org][Sagemath-övningar på kedjebråk]]
 - [[file:labs/HenselLyftLabHT2023.org][SageMath-övningar på Hensellyft, primitiva rötter, och KRS]]
-- [[file:lectures/Henselfaktorisering.org][Henselfaktorisering]]
\ No newline at end of file
+- [[file:newlectures/newlecture.org][Föreläsningar i Talteori]]
+- [[file:newlectures/new-lect-0.org][Talteori översiktsföreläsning]]
\ No newline at end of file
diff --git a/public/exams/2024/tenta-TATA54-20240822-losning.pdf b/public/exams/2024/tenta-TATA54-20240822-losning.pdf
new file mode 100644
index 0000000000000000000000000000000000000000..34f831aaf168f2a7b0660a02384565b351b6565c
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diff --git a/public/exams/2024/tenta-TATA54-20240822.pdf b/public/exams/2024/tenta-TATA54-20240822.pdf
new file mode 100644
index 0000000000000000000000000000000000000000..d839e73d319edc0de99e0682c720582432af21ae
Binary files /dev/null and b/public/exams/2024/tenta-TATA54-20240822.pdf differ
diff --git a/public/index.html b/public/index.html
index 0d3ec795cd56a7b2163eb5ca468688068381f743..311d8f664186b7eb807f162298c2e9388573f49c 100644
--- a/public/index.html
+++ b/public/index.html
@@ -1,7 +1,7 @@
 <!DOCTYPE html>
 <html lang="sv">
 <head>
-<!-- 2024-06-05 -->
+<!-- 2024-08-22 -->
 <meta charset="utf-8" />
 <meta name="viewport" content="width=device-width, initial-scale=1" />
 <title>TATA54 Talteori</title>
@@ -63,150 +63,150 @@
 <h2>Inneh&aring;ll</h2>
 <div id="text-table-of-contents" role="doc-toc">
 <ul>
-<li><a href="#org11cd8e4">Kurshemsida för TATA54, Talteori  </a>
+<li><a href="#orgb8be38a">Kurshemsida för TATA54, Talteori  </a>
 <ul>
-<li><a href="#orgbf145e8">Ämnesområde</a></li>
-<li><a href="#orgbd10c80">Poäng</a></li>
-<li><a href="#orgdf916de">Examinator</a></li>
-<li><a href="#org0e97f91">Schema</a></li>
-<li><a href="#org978acab">Examination</a></li>
+<li><a href="#org46c8838">Ämnesområde</a></li>
+<li><a href="#org0536e03">Poäng</a></li>
+<li><a href="#org483cd31">Examinator</a></li>
+<li><a href="#org79caf1d">Schema</a></li>
+<li><a href="#org3280174">Examination</a></li>
 </ul>
 </li>
-<li><a href="#orgc6ffe16">Allra senaste nytt VT2024 </a>
+<li><a href="#orge4d1d7b">Allra senaste nytt VT2024 </a>
 <ul>
-<li><a href="#orgd106c4f">2024-06-05</a></li>
-<li><a href="#orgba4c7fd">2024-06-01</a></li>
-<li><a href="#org2921027">2024-05-18</a></li>
-<li><a href="#org580c3f6">2024-05-16</a></li>
-<li><a href="#orgfb06446">2024-05-13</a></li>
-<li><a href="#org36a5a6c">2024-05-06</a></li>
-<li><a href="#orge2800f4">2024-04-29</a></li>
-<li><a href="#org8296c85">2024-04-23</a></li>
-<li><a href="#orgc936b6f">2024-04-22</a></li>
-<li><a href="#org4dc177a">2024-04-14</a>
+<li><a href="#org4de2404">2024-06-05</a></li>
+<li><a href="#org7866ed4">2024-06-01</a></li>
+<li><a href="#org896f14e">2024-05-18</a></li>
+<li><a href="#org016a4e1">2024-05-16</a></li>
+<li><a href="#org4232b8e">2024-05-13</a></li>
+<li><a href="#org95a2714">2024-05-06</a></li>
+<li><a href="#orgcae408e">2024-04-29</a></li>
+<li><a href="#org9f9d6f3">2024-04-23</a></li>
+<li><a href="#orgb23df4f">2024-04-22</a></li>
+<li><a href="#org6bf16cd">2024-04-14</a>
 <ul>
-<li><a href="#org0f556e1">Uppgifter att räkna till nästa gång</a></li>
-<li><a href="#orgbc6c0fd">Datorlaboration</a></li>
+<li><a href="#org919c9e5">Uppgifter att räkna till nästa gång</a></li>
+<li><a href="#orgef7eb4d">Datorlaboration</a></li>
 </ul>
 </li>
-<li><a href="#org865cc31">2024-04-07</a>
+<li><a href="#org4a80012">2024-04-07</a>
 <ul>
-<li><a href="#orga5ff711">Uppgifter att räkna till nästa gång</a></li>
-<li><a href="#org9f5a134">Beviset för kvadratisk reciprocitet</a></li>
+<li><a href="#orgfb7845d">Uppgifter att räkna till nästa gång</a></li>
+<li><a href="#orgd77ff3b">Beviset för kvadratisk reciprocitet</a></li>
 </ul>
 </li>
-<li><a href="#org429e5d4">2024-04-02</a></li>
-<li><a href="#orgfa53138">2024-03-11</a></li>
-<li><a href="#org54eab67">2024-03-06</a></li>
-<li><a href="#org73f95a7">2024-03-05</a></li>
-<li><a href="#orgf0c9193">2024-02-29</a></li>
-<li><a href="#org7f7d557">2024-02-20</a></li>
-<li><a href="#org6fc379e">2024-02-12</a></li>
-<li><a href="#org7b22a27">2024-02-07</a></li>
-<li><a href="#orgbc98f91">2024-01-30</a>
+<li><a href="#orgb250740">2024-04-02</a></li>
+<li><a href="#orged4ff0b">2024-03-11</a></li>
+<li><a href="#org0de71ab">2024-03-06</a></li>
+<li><a href="#org84eda8d">2024-03-05</a></li>
+<li><a href="#orgea6ed65">2024-02-29</a></li>
+<li><a href="#org823f5e2">2024-02-20</a></li>
+<li><a href="#org1c24ff1">2024-02-12</a></li>
+<li><a href="#org499023d">2024-02-07</a></li>
+<li><a href="#orgf683b42">2024-01-30</a>
 <ul>
-<li><a href="#org7ada8fb">Tvillingfria primtal</a></li>
+<li><a href="#org53dcc9b">Tvillingfria primtal</a></li>
 </ul>
 </li>
-<li><a href="#org5081bbc">2024-01-23</a></li>
-<li><a href="#orgec17e4b">2024-01-16</a></li>
+<li><a href="#orgd22b4e6">2024-01-23</a></li>
+<li><a href="#org5900f63">2024-01-16</a></li>
 </ul>
 </li>
-<li><a href="#org83cdbc2">Kurslitteratur </a>
+<li><a href="#org4f543bd">Kurslitteratur </a>
 <ul>
-<li><a href="#org969d2a9">Kursbok</a></li>
-<li><a href="#orgfa4a7ab">Bredvidläsning</a>
+<li><a href="#org09cac9a">Kursbok</a></li>
+<li><a href="#orgdf2c024">Bredvidläsning</a>
 <ul>
-<li><a href="#orge4da471">Fritt tillgängligt material</a></li>
-<li><a href="#org2169300">Andra lämpliga böcker</a></li>
+<li><a href="#org9934079">Fritt tillgängligt material</a></li>
+<li><a href="#org486a906">Andra lämpliga böcker</a></li>
 </ul>
 </li>
 </ul>
 </li>
-<li><a href="#orgc6c0ef4">Kursinnehåll </a>
+<li><a href="#org83d546e">Kursinnehåll </a>
 <ul>
-<li><a href="#org43c7b85">Avsnitt av kursboken</a>
+<li><a href="#org34795a7">Avsnitt av kursboken</a>
 <ul>
-<li><a href="#org0c49604">Rekommenderade uppgifter </a></li>
+<li><a href="#org10138de">Rekommenderade uppgifter </a></li>
 </ul>
 </li>
-<li><a href="#org33f6268">Kort beskrivning av kursinnehållet</a></li>
+<li><a href="#orgab0c2e2">Kort beskrivning av kursinnehållet</a></li>
 </ul>
 </li>
-<li><a href="#org0e51919">Föreläsningar </a></li>
-<li><a href="#orgf5fd67d">Tentor </a></li>
-<li><a href="#orgac41624">Datorlaborationer </a>
+<li><a href="#org67ef94b">Föreläsningar </a></li>
+<li><a href="#org9e66246">Tentor </a></li>
+<li><a href="#orgf236219">Datorlaborationer </a>
 <ul>
-<li><a href="#orgd0ccf06">SageMath</a></li>
-<li><a href="#orgd3b0180">Kod från vissa föreläsningar</a></li>
-<li><a href="#org85c34f4">Laborationer</a>
+<li><a href="#org7a98c02">SageMath</a></li>
+<li><a href="#org38724a4">Kod från vissa föreläsningar</a></li>
+<li><a href="#org80ba8f8">Laborationer</a>
 <ul>
-<li><a href="#orga1be7da">Hensellyft, Primitiva rötter, Kinesiska restsatsen</a></li>
-<li><a href="#org2528f16">Kedjebråk</a></li>
+<li><a href="#org4bb0ea2">Hensellyft, Primitiva rötter, Kinesiska restsatsen</a></li>
+<li><a href="#org4f8b714">Kedjebråk</a></li>
 </ul>
 </li>
 </ul>
 </li>
-<li><a href="#org27d49bb">Tidigare år </a>
+<li><a href="#org65b020a">Tidigare år </a>
 <ul>
-<li><a href="#orga1fa650">TATA54 Anteckningar från tidigare år</a>
+<li><a href="#org477262d">TATA54 Anteckningar från tidigare år</a>
 <ul>
-<li><a href="#orgd4aaf8a">2023</a></li>
-<li><a href="#orgc39991d">2021</a></li>
-<li><a href="#org6bff760">2020</a></li>
-<li><a href="#org85cd779">2019</a></li>
-<li><a href="#org21f5089">2018</a></li>
-<li><a href="#org7ce4987">2017</a></li>
+<li><a href="#org780ed90">2023</a></li>
+<li><a href="#org780092f">2021</a></li>
+<li><a href="#org2b03280">2020</a></li>
+<li><a href="#org9b6101f">2019</a></li>
+<li><a href="#orgba3d96f">2018</a></li>
+<li><a href="#org45290d5">2017</a></li>
 </ul>
 </li>
 </ul>
 </li>
-<li><a href="#orga44ea53">Index</a></li>
+<li><a href="#org22888c0">Index</a></li>
 </ul>
 </div>
 </nav>
 
-<section id="outline-container-org11cd8e4" class="outline-2">
-<h2 id="org11cd8e4">Kurshemsida för TATA54, Talteori  <a id="orgebfa722"></a></h2>
-<div class="outline-text-2" id="text-org11cd8e4">
+<section id="outline-container-orgb8be38a" class="outline-2">
+<h2 id="orgb8be38a">Kurshemsida för TATA54, Talteori  <a id="orgf086129"></a></h2>
+<div class="outline-text-2" id="text-orgb8be38a">
 </div>
-<div id="outline-container-orgbf145e8" class="outline-3">
-<h3 id="orgbf145e8">Ämnesområde</h3>
-<div class="outline-text-3" id="text-orgbf145e8">
+<div id="outline-container-org46c8838" class="outline-3">
+<h3 id="org46c8838">Ämnesområde</h3>
+<div class="outline-text-3" id="text-org46c8838">
 <p>
 Matematik
 </p>
 </div>
 </div>
-<div id="outline-container-orgbd10c80" class="outline-3">
-<h3 id="orgbd10c80">Poäng</h3>
-<div class="outline-text-3" id="text-orgbd10c80">
+<div id="outline-container-org0536e03" class="outline-3">
+<h3 id="org0536e03">Poäng</h3>
+<div class="outline-text-3" id="text-org0536e03">
 <p>
 6 hp
 </p>
 </div>
 </div>
-<div id="outline-container-orgdf916de" class="outline-3">
-<h3 id="orgdf916de">Examinator</h3>
-<div class="outline-text-3" id="text-orgdf916de">
+<div id="outline-container-org483cd31" class="outline-3">
+<h3 id="org483cd31">Examinator</h3>
+<div class="outline-text-3" id="text-org483cd31">
 <p>
 <a href="https://liu.se/medarbetare/jansn19">Jan Snellman</a> (se även min
 <a href="https://jansn19.gitlab-pages.liu.se/jan-snellman-hemsida/">hemsida</a>)
 </p>
 </div>
 </div>
-<div id="outline-container-org0e97f91" class="outline-3">
-<h3 id="org0e97f91">Schema</h3>
-<div class="outline-text-3" id="text-org0e97f91">
+<div id="outline-container-org79caf1d" class="outline-3">
+<h3 id="org79caf1d">Schema</h3>
+<div class="outline-text-3" id="text-org79caf1d">
 <p>
 Se <a href="https://cloud.timeedit.net/liu/web/schema/ri167XQQ538Z50Qm07065gZ6y2Y7306Q6Y43Y1.html">TimeEdit</a>
 </p>
 </div>
 </div>
 
-<div id="outline-container-org978acab" class="outline-3">
-<h3 id="org978acab">Examination</h3>
-<div class="outline-text-3" id="text-org978acab">
+<div id="outline-container-org3280174" class="outline-3">
+<h3 id="org3280174">Examination</h3>
+<div class="outline-text-3" id="text-org3280174">
 <p>
 Skriftlig tentamen.
 </p>
@@ -259,13 +259,13 @@ Skriftlig tentamen.
 </div>
 </div>
 </section>
-<section id="outline-container-orgc6ffe16" class="outline-2">
-<h2 id="orgc6ffe16">Allra senaste nytt VT2024 <a id="orgba15c0d"></a></h2>
-<div class="outline-text-2" id="text-orgc6ffe16">
+<section id="outline-container-orge4d1d7b" class="outline-2">
+<h2 id="orge4d1d7b">Allra senaste nytt VT2024 <a id="org3ff915a"></a></h2>
+<div class="outline-text-2" id="text-orge4d1d7b">
 </div>
-<div id="outline-container-orgd106c4f" class="outline-3">
-<h3 id="orgd106c4f">2024-06-05</h3>
-<div class="outline-text-3" id="text-orgd106c4f">
+<div id="outline-container-org4de2404" class="outline-3">
+<h3 id="org4de2404">2024-06-05</h3>
+<div class="outline-text-3" id="text-org4de2404">
 <p>
 Jag har rättat era tentor; bra resultat, de flesta klarade sig! Resultaten kommer
 sannolikt att registreras idag, och tentorna kan hämtas p MAIs expedition f.o.m.
@@ -273,18 +273,18 @@ nästa vecka.
 </p>
 </div>
 </div>
-<div id="outline-container-orgba4c7fd" class="outline-3">
-<h3 id="orgba4c7fd">2024-06-01</h3>
-<div class="outline-text-3" id="text-orgba4c7fd">
+<div id="outline-container-org7866ed4" class="outline-3">
+<h3 id="org7866ed4">2024-06-01</h3>
+<div class="outline-text-3" id="text-org7866ed4">
 <p>
 <a href="exams/2024/tenta-TATA54-20240601-losning.pdf">Lösningar</a> till <a href="exams/2024/tenta-TATA54-20240601.pdf">dagens tenta</a> finns nu att beskåda. Jag hoppas kunna rätta tentorna till på fredag nästa vecka.
 </p>
 </div>
 </div>
 
-<div id="outline-container-org2921027" class="outline-3">
-<h3 id="org2921027">2024-05-18</h3>
-<div class="outline-text-3" id="text-org2921027">
+<div id="outline-container-org896f14e" class="outline-3">
+<h3 id="org896f14e">2024-05-18</h3>
+<div class="outline-text-3" id="text-org896f14e">
 <p>
 Återstående lektion är inställd. Läs kursboken om Gaussiska heltal
 och summor av två kvadrater, titta på föreläsningsanteckningarna om  <a href="lectures/swelecture11.pdf">Gaussiska heltal</a>
@@ -295,13 +295,13 @@ ingår i kursen, som kongruenser modulo Gaussiska heltal.
 
 <p>
 Jag påminner om att kursens innehåll är specificerad som en lista av kapitel i
-Rosen, finns <a href="#org06fee11">längre ned på denna sida</a>.
+Rosen, finns <a href="#orge3aa510">längre ned på denna sida</a>.
 </p>
 </div>
 </div>
-<div id="outline-container-org580c3f6" class="outline-3">
-<h3 id="org580c3f6">2024-05-16</h3>
-<div class="outline-text-3" id="text-org580c3f6">
+<div id="outline-container-org016a4e1" class="outline-3">
+<h3 id="org016a4e1">2024-05-16</h3>
+<div class="outline-text-3" id="text-org016a4e1">
 <p>
 Jag är inlagd på sjukhus&#x2026; Det är väl osäkert om det går att hitta vikarier
 till lektionerna i morgon och på måndag. Fråga någon av studierektorerna, eller proprefekt Jesper Thoren.
@@ -312,35 +312,35 @@ Tentamen skall kunna bli av utan problem!
 </p>
 </div>
 </div>
-<div id="outline-container-orgfb06446" class="outline-3">
-<h3 id="orgfb06446">2024-05-13</h3>
-<div class="outline-text-3" id="text-orgfb06446">
+<div id="outline-container-org4232b8e" class="outline-3">
+<h3 id="org4232b8e">2024-05-13</h3>
+<div class="outline-text-3" id="text-org4232b8e">
 <p>
 Till på fredag så tittar vi på 13.4.3abc, 13.4.5, 13.4.11.
 Till sista lektionen (måndag 20 maj) så tittar vi på 14.1.17ab, 14.1.23.
 </p>
 </div>
 </div>
-<div id="outline-container-org36a5a6c" class="outline-3">
-<h3 id="org36a5a6c">2024-05-06</h3>
-<div class="outline-text-3" id="text-org36a5a6c">
+<div id="outline-container-org95a2714" class="outline-3">
+<h3 id="org95a2714">2024-05-06</h3>
+<div class="outline-text-3" id="text-org95a2714">
 <p>
 Till nästa gång så tittar vi på 13.1.15, 13.3.1.b, 13.3.2g, 13.3.6, 13.3.8.
 </p>
 </div>
 </div>
 
-<div id="outline-container-orge2800f4" class="outline-3">
-<h3 id="orge2800f4">2024-04-29</h3>
-<div class="outline-text-3" id="text-orge2800f4">
+<div id="outline-container-orgcae408e" class="outline-3">
+<h3 id="orgcae408e">2024-04-29</h3>
+<div class="outline-text-3" id="text-orgcae408e">
 <p>
 Till nästa gång så tittar vi på 12.4.3b, 12.4.8, 13.1.2, 13.1.3. 
 </p>
 </div>
 </div>
-<div id="outline-container-org8296c85" class="outline-3">
-<h3 id="org8296c85">2024-04-23</h3>
-<div class="outline-text-3" id="text-org8296c85">
+<div id="outline-container-org9f9d6f3" class="outline-3">
+<h3 id="org9f9d6f3">2024-04-23</h3>
+<div class="outline-text-3" id="text-org9f9d6f3">
 <p>
 Jag pratade om &rdquo;Eulers regel&rdquo; som uttrycker kedjebråkskonvergenterna
 q<sub>n</sub>/p<sub>n</sub> till [x<sub>0</sub>;x<sub>1,x</sub><sub>2,&hellip;</sub>] som rationella funktioner i
@@ -353,9 +353,9 @@ beskrivningen kan visas med induktion.
 </p>
 </div>
 </div>
-<div id="outline-container-orgc936b6f" class="outline-3">
-<h3 id="orgc936b6f">2024-04-22</h3>
-<div class="outline-text-3" id="text-orgc936b6f">
+<div id="outline-container-orgb23df4f" class="outline-3">
+<h3 id="orgb23df4f">2024-04-22</h3>
+<div class="outline-text-3" id="text-orgb23df4f">
 <p>
 Vi har två föreläsningar den kommande veckan, torsdag 24 april samt fredag 25 april.
 Till på torsdag tittar ni på 12.3.1c, 12.2.2a (nedskalad till första 4), 12.3.4 (nedskalat till första 5, approximationsfel &lt; 1/100).
@@ -363,21 +363,21 @@ Till på fredag 12.4.5b, 12.4.6b
 </p>
 </div>
 </div>
-<div id="outline-container-org4dc177a" class="outline-3">
-<h3 id="org4dc177a">2024-04-14</h3>
-<div class="outline-text-3" id="text-org4dc177a">
+<div id="outline-container-org6bf16cd" class="outline-3">
+<h3 id="org6bf16cd">2024-04-14</h3>
+<div class="outline-text-3" id="text-org6bf16cd">
 </div>
-<div id="outline-container-org0f556e1" class="outline-4">
-<h4 id="org0f556e1">Uppgifter att räkna till nästa gång</h4>
-<div class="outline-text-4" id="text-org0f556e1">
+<div id="outline-container-org919c9e5" class="outline-4">
+<h4 id="org919c9e5">Uppgifter att räkna till nästa gång</h4>
+<div class="outline-text-4" id="text-org919c9e5">
 <p>
 12.2.1bf, 12.2.2cd, 12.2.3c, 12.2.11
 </p>
 </div>
 </div>
-<div id="outline-container-orgbc6c0fd" class="outline-4">
-<h4 id="orgbc6c0fd">Datorlaboration</h4>
-<div class="outline-text-4" id="text-orgbc6c0fd">
+<div id="outline-container-orgef7eb4d" class="outline-4">
+<h4 id="orgef7eb4d">Datorlaboration</h4>
+<div class="outline-text-4" id="text-orgef7eb4d">
 <p>
 Titta på <a href="labs/kedjebraklabweb.html">kedjebråkslabben</a> och använd den för att göra 12.2.3df.
 Hitta en formel för a(k,m) = [k;k,&#x2026;,k] (längd m). Vad är
@@ -386,21 +386,21 @@ gränsvärdet av a(k,m) då m går mot oändligheten?
 </div>
 </div>
 </div>
-<div id="outline-container-org865cc31" class="outline-3">
-<h3 id="org865cc31">2024-04-07</h3>
-<div class="outline-text-3" id="text-org865cc31">
+<div id="outline-container-org4a80012" class="outline-3">
+<h3 id="org4a80012">2024-04-07</h3>
+<div class="outline-text-3" id="text-org4a80012">
 </div>
-<div id="outline-container-orga5ff711" class="outline-4">
-<h4 id="orga5ff711">Uppgifter att räkna till nästa gång</h4>
-<div class="outline-text-4" id="text-orga5ff711">
+<div id="outline-container-orgfb7845d" class="outline-4">
+<h4 id="orgfb7845d">Uppgifter att räkna till nästa gång</h4>
+<div class="outline-text-4" id="text-orgfb7845d">
 <p>
 11.1.1d, 11.1.4, 11.1.25ab, 11.2.1cd, 11.2.2, 11.2.3,11.2.4
 </p>
 </div>
 </div>
-<div id="outline-container-org9f5a134" class="outline-4">
-<h4 id="org9f5a134">Beviset för kvadratisk reciprocitet</h4>
-<div class="outline-text-4" id="text-org9f5a134">
+<div id="outline-container-orgd77ff3b" class="outline-4">
+<h4 id="orgd77ff3b">Beviset för kvadratisk reciprocitet</h4>
+<div class="outline-text-4" id="text-orgd77ff3b">
 <p>
 Jag stakade mig lite vid bevist för kvadratisk reciprocitet. Speciellt så oroade jag mig över
 om det kunde finnas gitterpunkter (x,y) med x=(p-1)/2, (q-1)/2 &lt; y &lt;= (q/p)x.
@@ -409,17 +409,17 @@ Men det är enkelt att visa att (p-1)/2*q &lt; (q-1)2 +1, så det går inte. Bev
 </div>
 </div>
 </div>
-<div id="outline-container-org429e5d4" class="outline-3">
-<h3 id="org429e5d4">2024-04-02</h3>
-<div class="outline-text-3" id="text-org429e5d4">
+<div id="outline-container-orgb250740" class="outline-3">
+<h3 id="orgb250740">2024-04-02</h3>
+<div class="outline-text-3" id="text-orgb250740">
 <p>
 På fredag så räknar vi de uppgifter om diskreta logaritmer vi inte hann med förra gången.
 </p>
 </div>
 </div>
-<div id="outline-container-orgfa53138" class="outline-3">
-<h3 id="orgfa53138">2024-03-11</h3>
-<div class="outline-text-3" id="text-orgfa53138">
+<div id="outline-container-orged4ff0b" class="outline-3">
+<h3 id="orged4ff0b">2024-03-11</h3>
+<div class="outline-text-3" id="text-orged4ff0b">
 <p>
 Jag har nu bokat om föreläsningarna till Fredagar kl 13-15 (fortfarande i kompakta rummet)
 samt måndag 25 mars kl 13-15,
@@ -428,9 +428,9 @@ Det blir 10 tillfällen totalt, vilket bör räcka.
 </p>
 </div>
 </div>
-<div id="outline-container-org54eab67" class="outline-3">
-<h3 id="org54eab67">2024-03-06</h3>
-<div class="outline-text-3" id="text-org54eab67">
+<div id="outline-container-org0de71ab" class="outline-3">
+<h3 id="org0de71ab">2024-03-06</h3>
+<div class="outline-text-3" id="text-org0de71ab">
 <p>
 Det verkar som fredagar kl 13-15 inte kolliderar med andra kurser, så jag planerar att flytta lektioner till den tiden.
 Det är 8 sådana fredagar under perioden, så helst skall jag schemalägga tre tillfällen till.
@@ -439,9 +439,9 @@ Möjliga tider är måndag 25 mars kl 13-15, torsdag 25 april kl 13-15, måndag
 </p>
 </div>
 </div>
-<div id="outline-container-org73f95a7" class="outline-3">
-<h3 id="org73f95a7">2024-03-05</h3>
-<div class="outline-text-3" id="text-org73f95a7">
+<div id="outline-container-org84eda8d" class="outline-3">
+<h3 id="org84eda8d">2024-03-05</h3>
+<div class="outline-text-3" id="text-org84eda8d">
 <p>
 Det har framförts önskemål om att byta tid för lektionerna i period 4 för att undvika
 kollision med kursen i optimeringslära.
@@ -462,9 +462,9 @@ Det rör sig om 11 tillfällen totalt.
 </p>
 </div>
 </div>
-<div id="outline-container-orgf0c9193" class="outline-3">
-<h3 id="orgf0c9193">2024-02-29</h3>
-<div class="outline-text-3" id="text-orgf0c9193">
+<div id="outline-container-orgea6ed65" class="outline-3">
+<h3 id="orgea6ed65">2024-02-29</h3>
+<div class="outline-text-3" id="text-orgea6ed65">
 <p>
 Till nästa lektion så tittar ni på uppgifterna
 9.1.1d, 9.1.2d, 9.1.5b, 9.1.6d, 9.1.10, 9.1.20.
@@ -478,9 +478,9 @@ Till lektionen efter det (27 mars) så räknar ni
 </div>
 </div>
 
-<div id="outline-container-org7f7d557" class="outline-3">
-<h3 id="org7f7d557">2024-02-20</h3>
-<div class="outline-text-3" id="text-org7f7d557">
+<div id="outline-container-org823f5e2" class="outline-3">
+<h3 id="org823f5e2">2024-02-20</h3>
+<div class="outline-text-3" id="text-org823f5e2">
 <p>
 Till nästa lektion (27 feb) så tittar ni på uppgifterna
 4.2.15, 4.2.16, 4.2.18, 4.4.2ab. Använd Hensels lemma vid behov.
@@ -491,7 +491,7 @@ grad 5 eller 6.
 </p>
 
 <div class="org-src-container">
-<pre class="src src-sage" id="org4d90c6b">def H_L_tree(f, p: int, r: int):
+<pre class="src src-sage" id="orgce6ce24">def H_L_tree(f, p: int, r: int):
 
     vert = [(0,0)]
     for j in range(1,r+1):
@@ -520,25 +520,25 @@ H_L_tree(f,p,r).plot(layout='tree')
 </div>
 
 
-<figure id="orgd0b857d">
+<figure id="orgcf88db9">
 <img src="img/Henseluppgift.png" alt="Henseluppgift.png">
 
 </figure>
 </div>
 </div>
 
-<div id="outline-container-org6fc379e" class="outline-3">
-<h3 id="org6fc379e">2024-02-12</h3>
-<div class="outline-text-3" id="text-org6fc379e">
+<div id="outline-container-org1c24ff1" class="outline-3">
+<h3 id="org1c24ff1">2024-02-12</h3>
+<div class="outline-text-3" id="text-org1c24ff1">
 <p>
 Till nästa lektion (20 feb) så tittar ni på uppgifterna
 7.1.5, 7.2.1d, 7.2.8, 7.2.35, 7.4.23, 7.4.24
 </p>
 </div>
 </div>
-<div id="outline-container-org7b22a27" class="outline-3">
-<h3 id="org7b22a27">2024-02-07</h3>
-<div class="outline-text-3" id="text-org7b22a27">
+<div id="outline-container-org499023d" class="outline-3">
+<h3 id="org499023d">2024-02-07</h3>
+<div class="outline-text-3" id="text-org499023d">
 <p>
 Till nästa lektion (12 feb) så tittar ni på uppgifterna
 4.1.5, 4.1.9b, 4.2.8c,4.3.3.
@@ -548,9 +548,9 @@ att vara i Kompakta rummet.
 </div>
 </div>
 
-<div id="outline-container-orgbc98f91" class="outline-3">
-<h3 id="orgbc98f91">2024-01-30</h3>
-<div class="outline-text-3" id="text-orgbc98f91">
+<div id="outline-container-orgf683b42" class="outline-3">
+<h3 id="orgf683b42">2024-01-30</h3>
+<div class="outline-text-3" id="text-orgf683b42">
 <ul class="org-ul">
 <li>Till nästa gång så tittar ni på uppgifterna 3.3.10, 3.4.1c,3.4.20, 3.5.32,3.7.1c</li>
 <li>Dessutom: visa att om \(m,n\) relativt prima, \(m|a\), \(n|a\), så \(mn|a\).</li>
@@ -559,9 +559,9 @@ att vara i Kompakta rummet.
 </ul>
 </div>
 
-<div id="outline-container-org7ada8fb" class="outline-4">
-<h4 id="org7ada8fb">Tvillingfria primtal</h4>
-<div class="outline-text-4" id="text-org7ada8fb">
+<div id="outline-container-org53dcc9b" class="outline-4">
+<h4 id="org53dcc9b">Tvillingfria primtal</h4>
+<div class="outline-text-4" id="text-org53dcc9b">
 <p>
 Jag använde följande sagemath-kod för att hitta \((k,n)\) med
 sgd(k,n)=1, sgd(k-2,n) &gt; 1, sgd(k+2,n) &gt;1, så att Dirichlets sats
@@ -569,7 +569,7 @@ garanterar oändligt många primtal i nZ + k.
 </p>
 
 <div class="org-src-container">
-<pre class="src src-sage" id="org1e013cf">def repr(n):
+<pre class="src src-sage" id="org400f273">def repr(n):
     return [k for k in range(n) if gcd(k,n)==1]
 
 def isolated(n):
@@ -600,17 +600,17 @@ Körning visar att n=15, k=7 är minsta exemplet.
 </div>
 </div>
 
-<div id="outline-container-org5081bbc" class="outline-3">
-<h3 id="org5081bbc">2024-01-23</h3>
-<div class="outline-text-3" id="text-org5081bbc">
+<div id="outline-container-orgd22b4e6" class="outline-3">
+<h3 id="orgd22b4e6">2024-01-23</h3>
+<div class="outline-text-3" id="text-orgd22b4e6">
 <p>
 Till nästa gång så tittar ni på uppgifterna 1.5.18, 1.5.36, 3.1.6, 3.2.10.
 </p>
 </div>
 </div>
-<div id="outline-container-orgec17e4b" class="outline-3">
-<h3 id="orgec17e4b">2024-01-16</h3>
-<div class="outline-text-3" id="text-orgec17e4b">
+<div id="outline-container-org5900f63" class="outline-3">
+<h3 id="org5900f63">2024-01-16</h3>
+<div class="outline-text-3" id="text-org5900f63">
 <ul class="org-ul">
 <li>Första föreläsningen, information om kursupplägget, kurslitteratur, tentamen.</li>
 <li>Pratade om <a href="lectures/swelecture0.pdf">talteori som matematisk disciplin</a>, mycket översiktligt.</li>
@@ -618,7 +618,7 @@ Till nästa gång så tittar ni på uppgifterna 1.5.18, 1.5.36, 3.1.6, 3.2.10.
 <li>Önskemål om information om vilka/vilket kapitel i kursboken en given
 föreläsning är kopplad till, skall ordna.</li>
 <li>Vi kommer att gå igenom uppgifter
-(hämtade från listan med <a href="#orgd99cfc5">rekommenderade uppgifter</a>)
+(hämtade från listan med <a href="#org7db4ce4">rekommenderade uppgifter</a>)
 på vissa av lektionstillfällena, kanske första 45 minuterna. Annonseras här.</li>
 <li>Jag glömde att framföra följande förmaning: även om kursen examineras med en enda skriftlig
 tentamen i juni så är det viktigt att studera kontinuerligt, och räkna uppgifter.
@@ -632,19 +632,19 @@ till, nu med fokus på att förstå bevisen.</li>
 </div>
 </section>
 
-<section id="outline-container-org83cdbc2" class="outline-2">
-<h2 id="org83cdbc2">Kurslitteratur <a id="org47e9684"></a></h2>
-<div class="outline-text-2" id="text-org83cdbc2">
+<section id="outline-container-org4f543bd" class="outline-2">
+<h2 id="org4f543bd">Kurslitteratur <a id="org98e7bee"></a></h2>
+<div class="outline-text-2" id="text-org4f543bd">
 </div>
-<div id="outline-container-org969d2a9" class="outline-3">
-<h3 id="org969d2a9">Kursbok</h3>
-<div class="outline-text-3" id="text-org969d2a9">
+<div id="outline-container-org09cac9a" class="outline-3">
+<h3 id="org09cac9a">Kursbok</h3>
+<div class="outline-text-3" id="text-org09cac9a">
 <p>
 Kursbok är <a href="https://www.prisjakt.nu/produkt.php?p=8083662">Elementary Number Theory</a> av Kenneth Rosen.
 </p>
 
 
-<figure id="orgc8a4fed">
+<figure id="org09cfcfd">
 <img src="img/Rosen6ed.png" alt="Rosen6ed.png" width="40%">
 
 <figcaption><span class="figure-number">Illustration 1 </span>Elementary Number Theory, Kenneth Rosen</figcaption>
@@ -656,13 +656,13 @@ vilket inte påverkar innehållet.
 </p>
 </div>
 </div>
-<div id="outline-container-orgfa4a7ab" class="outline-3">
-<h3 id="orgfa4a7ab">Bredvidläsning</h3>
-<div class="outline-text-3" id="text-orgfa4a7ab">
+<div id="outline-container-orgdf2c024" class="outline-3">
+<h3 id="orgdf2c024">Bredvidläsning</h3>
+<div class="outline-text-3" id="text-orgdf2c024">
 </div>
-<div id="outline-container-orge4da471" class="outline-4">
-<h4 id="orge4da471">Fritt tillgängligt material</h4>
-<div class="outline-text-4" id="text-orge4da471">
+<div id="outline-container-org9934079" class="outline-4">
+<h4 id="org9934079">Fritt tillgängligt material</h4>
+<div class="outline-text-4" id="text-org9934079">
 <p>
 Följande böcker är fritt tillgängliga på nätet. Kursboken är väldigt grundlig
 och täcker kursinnehållet, men det kan ändå vara bra att se olika
@@ -680,9 +680,9 @@ Jolly för en metod att hitta primitiva rötter.</li>
 </ul>
 </div>
 </div>
-<div id="outline-container-org2169300" class="outline-4">
-<h4 id="org2169300">Andra lämpliga böcker</h4>
-<div class="outline-text-4" id="text-org2169300">
+<div id="outline-container-org486a906" class="outline-4">
+<h4 id="org486a906">Andra lämpliga böcker</h4>
+<div class="outline-text-4" id="text-org486a906">
 <ul class="org-ul">
 <li>BAKER. A concise introduction to the theory of numbers.</li>
 <li>DAVENPORT. The higher arithmetic.</li>
@@ -702,13 +702,13 @@ fortbildning efter denna kurs.</li>
 
 
 
-<section id="outline-container-orgc6c0ef4" class="outline-2">
-<h2 id="orgc6c0ef4">Kursinnehåll <a id="org06fee11"></a></h2>
-<div class="outline-text-2" id="text-orgc6c0ef4">
+<section id="outline-container-org83d546e" class="outline-2">
+<h2 id="org83d546e">Kursinnehåll <a id="orge3aa510"></a></h2>
+<div class="outline-text-2" id="text-org83d546e">
 </div>
-<div id="outline-container-org43c7b85" class="outline-3">
-<h3 id="org43c7b85">Avsnitt av kursboken</h3>
-<div class="outline-text-3" id="text-org43c7b85">
+<div id="outline-container-org34795a7" class="outline-3">
+<h3 id="org34795a7">Avsnitt av kursboken</h3>
+<div class="outline-text-3" id="text-org34795a7">
 <p>
 Kursen omfattar följande delar/kapitel av kursboken: 1.5, 2.1, 3, 4.1-4.4, 5.1,
 6, 7.1-7.4, 9, 11.1-11.4, 12, 13.1-13.4,14. Jag kommer inte att föreläsa om
@@ -718,15 +718,15 @@ från just dessa avsnitt.
 </p>
 </div>
 
-<div id="outline-container-org0c49604" class="outline-4">
-<h4 id="org0c49604">Rekommenderade uppgifter <a id="orgd99cfc5"></a></h4>
-<div class="outline-text-4" id="text-org0c49604">
+<div id="outline-container-org10138de" class="outline-4">
+<h4 id="org10138de">Rekommenderade uppgifter <a id="org7db4ce4"></a></h4>
+<div class="outline-text-4" id="text-org10138de">
 </div>
 <ul class="org-ul">
-<li><a id="org1cc7e3a"></a>Kap 1<br>
+<li><a id="org15b8e33"></a>Kap 1<br>
 <ul class="org-ul">
-<li><a id="org978ec51"></a>1.5<br>
-<div class="outline-text-6" id="text-org978ec51">
+<li><a id="orgb33f2f0"></a>1.5<br>
+<div class="outline-text-6" id="text-orgb33f2f0">
 <p>
 8a,9b,18,36,37
 </p>
@@ -734,46 +734,46 @@ från just dessa avsnitt.
 </li>
 </ul>
 </li>
-<li><a id="org0585282"></a>Kap 3<br>
+<li><a id="org681038a"></a>Kap 3<br>
 <ul class="org-ul">
-<li><a id="orgba991bb"></a>3.1<br>
-<div class="outline-text-6" id="text-orgba991bb">
+<li><a id="org0f22bbf"></a>3.1<br>
+<div class="outline-text-6" id="text-org0f22bbf">
 <p>
 1ab, 2f,6.
 </p>
 </div>
 </li>
-<li><a id="org1d83cec"></a>3.2<br>
-<div class="outline-text-6" id="text-org1d83cec">
+<li><a id="orga37167f"></a>3.2<br>
+<div class="outline-text-6" id="text-orga37167f">
 <ol class="org-ol">
 <li></li>
 </ol>
 </div>
 </li>
-<li><a id="org1f58297"></a>3.3<br>
-<div class="outline-text-6" id="text-org1f58297">
+<li><a id="orgb03bced"></a>3.3<br>
+<div class="outline-text-6" id="text-orgb03bced">
 <p>
 1df,2ef,10,24,30,31
 </p>
 </div>
 </li>
-<li><a id="org658bec3"></a>3.4<br>
-<div class="outline-text-6" id="text-org658bec3">
+<li><a id="orgec1beae"></a>3.4<br>
+<div class="outline-text-6" id="text-orgec1beae">
 <p>
 1bc, 19*, 20*.
 </p>
 </div>
 </li>
-<li><a id="orgb0fdc9e"></a>3.5<br>
-<div class="outline-text-6" id="text-orgb0fdc9e">
+<li><a id="orgcb8a7bd"></a>3.5<br>
+<div class="outline-text-6" id="text-orgcb8a7bd">
 <p>
 1il, 2, 4c, 29cd,
   32*, 34, 58ac.
 </p>
 </div>
 </li>
-<li><a id="org45b4d99"></a>3.7<br>
-<div class="outline-text-6" id="text-org45b4d99">
+<li><a id="orga2dfbe1"></a>3.7<br>
+<div class="outline-text-6" id="text-orga2dfbe1">
 <p>
 1cd
 </p>
@@ -781,31 +781,31 @@ från just dessa avsnitt.
 </li>
 </ul>
 </li>
-<li><a id="orgbb7b14d"></a>Kap 4<br>
+<li><a id="org37c2a66"></a>Kap 4<br>
 <ul class="org-ul">
-<li><a id="org06c1fef"></a>4.1<br>
-<div class="outline-text-6" id="text-org06c1fef">
+<li><a id="org6253340"></a>4.1<br>
+<div class="outline-text-6" id="text-org6253340">
 <p>
 4,5,7ab,9bc.
 </p>
 </div>
 </li>
-<li><a id="org53f1544"></a>4.2<br>
-<div class="outline-text-6" id="text-org53f1544">
+<li><a id="org54fbae8"></a>4.2<br>
+<div class="outline-text-6" id="text-org54fbae8">
 <p>
 1df, 8c, 9d.
 </p>
 </div>
 </li>
-<li><a id="org490796e"></a>4.3<br>
-<div class="outline-text-6" id="text-org490796e">
+<li><a id="org5ae1ea7"></a>4.3<br>
+<div class="outline-text-6" id="text-org5ae1ea7">
 <p>
 3,4.
 </p>
 </div>
 </li>
-<li><a id="orgb4590fd"></a>4.4<br>
-<div class="outline-text-6" id="text-orgb4590fd">
+<li><a id="org7fb6f3a"></a>4.4<br>
+<div class="outline-text-6" id="text-org7fb6f3a">
 <p>
 2ab.
 </p>
@@ -813,10 +813,10 @@ från just dessa avsnitt.
 </li>
 </ul>
 </li>
-<li><a id="org8aea6f0"></a>Kap 5<br>
+<li><a id="org67c0b01"></a>Kap 5<br>
 <ul class="org-ul">
-<li><a id="org34987f8"></a>5.1<br>
-<div class="outline-text-6" id="text-org34987f8">
+<li><a id="org72b5624"></a>5.1<br>
+<div class="outline-text-6" id="text-org72b5624">
 <p>
 4ab.
 </p>
@@ -824,26 +824,26 @@ från just dessa avsnitt.
 </li>
 </ul>
 </li>
-<li><a id="org44c4796"></a>Kap 6<br>
+<li><a id="org3e672b9"></a>Kap 6<br>
 <ul class="org-ul">
-<li><a id="org5467c3d"></a>6.1<br>
-<div class="outline-text-6" id="text-org5467c3d">
+<li><a id="org1f56359"></a>6.1<br>
+<div class="outline-text-6" id="text-org1f56359">
 <p>
 4,5,6,9,10,14,18,19,22,24,24,28,36,38*,41,48*,52.
 </p>
 </div>
 </li>
 
-<li><a id="orgcb44edd"></a>6.2<br>
-<div class="outline-text-6" id="text-orgcb44edd">
+<li><a id="org6facf0b"></a>6.2<br>
+<div class="outline-text-6" id="text-org6facf0b">
 <p>
 2,8,12,16ab.
 </p>
 </div>
 </li>
 
-<li><a id="orga80d292"></a>6.3<br>
-<div class="outline-text-6" id="text-orga80d292">
+<li><a id="org3eb9c1b"></a>6.3<br>
+<div class="outline-text-6" id="text-org3eb9c1b">
 <p>
 1d,6,7,22*
 </p>
@@ -852,31 +852,31 @@ från just dessa avsnitt.
 </ul>
 </li>
 
-<li><a id="orgdcdc40f"></a>Kap 7<br>
+<li><a id="orgdc43d50"></a>Kap 7<br>
 <ul class="org-ul">
-<li><a id="org90dcdab"></a>7.1<br>
-<div class="outline-text-6" id="text-org90dcdab">
+<li><a id="org70452c6"></a>7.1<br>
+<div class="outline-text-6" id="text-org70452c6">
 <p>
 2bc,5,8.
 </p>
 </div>
 </li>
-<li><a id="org39c711c"></a>7.2<br>
-<div class="outline-text-6" id="text-org39c711c">
+<li><a id="org613722d"></a>7.2<br>
+<div class="outline-text-6" id="text-org613722d">
 <p>
 1bd,2cd,8,34*,35,38*.
 </p>
 </div>
 </li>
-<li><a id="org2d9e7af"></a>7.3<br>
-<div class="outline-text-6" id="text-org2d9e7af">
+<li><a id="orgf2f87e9"></a>7.3<br>
+<div class="outline-text-6" id="text-orgf2f87e9">
 <p>
 3b,4,7,8,10,18,22**,28*,29cd.
 </p>
 </div>
 </li>
-<li><a id="org01dd2e1"></a>7.4<br>
-<div class="outline-text-6" id="text-org01dd2e1">
+<li><a id="org540c16c"></a>7.4<br>
+<div class="outline-text-6" id="text-org540c16c">
 <p>
 1bd,2be,14,22,23,24,30,31.
 </p>
@@ -885,47 +885,47 @@ från just dessa avsnitt.
 </ul>
 </li>
 
-<li><a id="org22e6c42"></a>Kap 9<br>
+<li><a id="orgd525786"></a>Kap 9<br>
 <ul class="org-ul">
-<li><a id="org3171b1b"></a>9.1<br>
-<div class="outline-text-6" id="text-org3171b1b">
+<li><a id="org8894071"></a>9.1<br>
+<div class="outline-text-6" id="text-org8894071">
 <p>
  1ad, 2cd, 5b, 6df, 8, 10, 20*,
 22*.
 </p>
 </div>
 </li>
-<li><a id="org9d9f07a"></a>9.2<br>
-<div class="outline-text-6" id="text-org9d9f07a">
+<li><a id="org68316e6"></a>9.2<br>
+<div class="outline-text-6" id="text-org68316e6">
 <p>
 1d, 2d, 3e, 6.
 </p>
 </div>
 </li>
-<li><a id="orgf0b7847"></a>9.3<br>
-<div class="outline-text-6" id="text-orgf0b7847">
+<li><a id="orgabc73c3"></a>9.3<br>
+<div class="outline-text-6" id="text-orgabc73c3">
 <p>
 2,3c, 5c,6c, 8b, 10.
 </p>
 </div>
 </li>
-<li><a id="org9f8fe1f"></a>9.4<br>
-<div class="outline-text-6" id="text-org9f8fe1f">
+<li><a id="org63ae623"></a>9.4<br>
+<div class="outline-text-6" id="text-org63ae623">
 <p>
 1, 2b, 3a,
   4, 9, 10, 19, 20*.
 </p>
 </div>
 </li>
-<li><a id="org99d1763"></a>9.5<br>
-<div class="outline-text-6" id="text-org99d1763">
+<li><a id="org9c13bc0"></a>9.5<br>
+<div class="outline-text-6" id="text-org9c13bc0">
 <p>
 2,3,10.
 </p>
 </div>
 </li>
-<li><a id="orgfa55cb8"></a>9.6<br>
-<div class="outline-text-6" id="text-orgfa55cb8">
+<li><a id="org5015ce5"></a>9.6<br>
+<div class="outline-text-6" id="text-org5015ce5">
 <p>
 1bcg, 4def, 13*, 14*.
 </p>
@@ -934,31 +934,31 @@ från just dessa avsnitt.
 </ul>
 </li>
 
-<li><a id="org94cf781"></a>Kap 11<br>
+<li><a id="org82f34bf"></a>Kap 11<br>
 <ul class="org-ul">
-<li><a id="org7d092f2"></a>11.1<br>
-<div class="outline-text-6" id="text-org7d092f2">
+<li><a id="org3d2f276"></a>11.1<br>
+<div class="outline-text-6" id="text-org3d2f276">
 <p>
 1d, 4, 25.
 </p>
 </div>
 </li>
-<li><a id="org88bf99e"></a>11.2<br>
-<div class="outline-text-6" id="text-org88bf99e">
+<li><a id="orgc0c01e2"></a>11.2<br>
+<div class="outline-text-6" id="text-orgc0c01e2">
 <p>
 1cd, 2, 4, 5.
 </p>
 </div>
 </li>
-<li><a id="org01d2881"></a>11.3<br>
-<div class="outline-text-6" id="text-org01d2881">
+<li><a id="org1af5d6e"></a>11.3<br>
+<div class="outline-text-6" id="text-org1af5d6e">
 <p>
 1ef, 5, 6.
 </p>
 </div>
 </li>
-<li><a id="orgad3a1ae"></a>11.4<br>
-<div class="outline-text-6" id="text-orgad3a1ae">
+<li><a id="orgfe1e34d"></a>11.4<br>
+<div class="outline-text-6" id="text-orgfe1e34d">
 <p>
 1, 2, 5, 6.
 </p>
@@ -967,32 +967,32 @@ från just dessa avsnitt.
 </ul>
 </li>
 
-<li><a id="org44aa093"></a>Kap 12<br>
+<li><a id="org2cc3178"></a>Kap 12<br>
 <ul class="org-ul">
-<li><a id="org936a20d"></a>12.2<br>
-<div class="outline-text-6" id="text-org936a20d">
+<li><a id="org7cac01e"></a>12.2<br>
+<div class="outline-text-6" id="text-org7cac01e">
 <p>
 1bf, 2cd, 3c, 4c.
 </p>
 </div>
 </li>
-<li><a id="org30d8efe"></a>12.3<br>
-<div class="outline-text-6" id="text-org30d8efe">
+<li><a id="orgb90f3a1"></a>12.3<br>
+<div class="outline-text-6" id="text-orgb90f3a1">
 <p>
 1c, 2a, 6*, 7.
 </p>
 </div>
 </li>
-<li><a id="orgc28fd4b"></a>12.4<br>
-<div class="outline-text-6" id="text-orgc28fd4b">
+<li><a id="orgca93be0"></a>12.4<br>
+<div class="outline-text-6" id="text-orgca93be0">
 <p>
 1c, 2c, 3b, 4a,
   5b, 6b, 7b,  8, 10, 17.
 </p>
 </div>
 </li>
-<li><a id="org6fe52f2"></a>12.5<br>
-<div class="outline-text-6" id="text-org6fe52f2">
+<li><a id="org677f1bb"></a>12.5<br>
+<div class="outline-text-6" id="text-org677f1bb">
 <ol class="org-ol">
 <li></li>
 </ol>
@@ -1001,32 +1001,32 @@ från just dessa avsnitt.
 </ul>
 </li>
 
-<li><a id="org3f74cbe"></a>Kap 13<br>
+<li><a id="orgedd8e06"></a>Kap 13<br>
 <ul class="org-ul">
-<li><a id="orgd9fc89a"></a>13.1<br>
-<div class="outline-text-6" id="text-orgd9fc89a">
+<li><a id="orgbcdde20"></a>13.1<br>
+<div class="outline-text-6" id="text-orgbcdde20">
 <p>
 1, 2, 3, 8, 16.
 </p>
 </div>
 </li>
-<li><a id="org80effe7"></a>13.2<br>
-<div class="outline-text-6" id="text-org80effe7">
+<li><a id="org8e3a488"></a>13.2<br>
+<div class="outline-text-6" id="text-org8e3a488">
 <p>
 3, 4,
   6*, 8, 10, 11*, 20.
 </p>
 </div>
 </li>
-<li><a id="orgc699f00"></a>13.3<br>
-<div class="outline-text-6" id="text-orgc699f00">
+<li><a id="org528308d"></a>13.3<br>
+<div class="outline-text-6" id="text-org528308d">
 <p>
 1b, 2gh,3cd, 6, 7, 9c, 10ef.
 </p>
 </div>
 </li>
-<li><a id="orgb9e9b7b"></a>13.4<br>
-<div class="outline-text-6" id="text-orgb9e9b7b">
+<li><a id="orgf68bc5b"></a>13.4<br>
+<div class="outline-text-6" id="text-orgf68bc5b">
 <p>
 1c,
   2a, 3def, 4ab, 6de, 8*.
@@ -1036,25 +1036,25 @@ från just dessa avsnitt.
 </ul>
 </li>
 
-<li><a id="org1a1cc94"></a>Kap 14<br>
+<li><a id="orgdcc1ad3"></a>Kap 14<br>
 <ul class="org-ul">
-<li><a id="org8bd881e"></a>14.1<br>
-<div class="outline-text-6" id="text-org8bd881e">
+<li><a id="org59fea14"></a>14.1<br>
+<div class="outline-text-6" id="text-org59fea14">
 <p>
 1ac, 12, 13, 17a.
 </p>
 </div>
 </li>
-<li><a id="org659103e"></a>14.2<br>
-<div class="outline-text-6" id="text-org659103e">
+<li><a id="orgb5250d8"></a>14.2<br>
+<div class="outline-text-6" id="text-orgb5250d8">
 <p>
 16ab,
   17bc.
 </p>
 </div>
 </li>
-<li><a id="org20cf5b1"></a>14.3<br>
-<div class="outline-text-6" id="text-org20cf5b1">
+<li><a id="org3675a33"></a>14.3<br>
+<div class="outline-text-6" id="text-org3675a33">
 <p>
 1bc, 2c
 </p>
@@ -1066,15 +1066,15 @@ från just dessa avsnitt.
 </div>
 </div>
 
-<div id="outline-container-org33f6268" class="outline-3">
-<h3 id="org33f6268">Kort beskrivning av kursinnehållet</h3>
+<div id="outline-container-orgab0c2e2" class="outline-3">
+<h3 id="orgab0c2e2">Kort beskrivning av kursinnehållet</h3>
 </div>
 </section>
 
 
-<section id="outline-container-org0e51919" class="outline-2">
-<h2 id="org0e51919">Föreläsningar <a id="org025d360"></a></h2>
-<div class="outline-text-2" id="text-org0e51919">
+<section id="outline-container-org67ef94b" class="outline-2">
+<h2 id="org67ef94b">Föreläsningar <a id="orgb94c813"></a></h2>
+<div class="outline-text-2" id="text-org67ef94b">
 <p>
 Jag har föreläst enligt följande föreläsningsanteckningar, med vissa utsvävningar.
 De svenska versionerna är nyare. Några av föreläsningarna tar två tillfällen för att gå igenom.
@@ -1253,9 +1253,9 @@ De svenska versionerna är nyare. Några av föreläsningarna tar två tillfäll
 </section>
 
 
-<section id="outline-container-orgf5fd67d" class="outline-2">
-<h2 id="orgf5fd67d">Tentor <a id="org64fbaef"></a></h2>
-<div class="outline-text-2" id="text-orgf5fd67d">
+<section id="outline-container-org9e66246" class="outline-2">
+<h2 id="org9e66246">Tentor <a id="orgcbd53f3"></a></h2>
+<div class="outline-text-2" id="text-org9e66246">
 <table>
 
 
@@ -1277,6 +1277,13 @@ De svenska versionerna är nyare. Några av föreläsningarna tar två tillfäll
 </tr>
 </thead>
 <tbody>
+<tr>
+<td class="org-right">2024-08-22</td>
+<td class="org-left">Jan Snellman</td>
+<td class="org-left"><a href="exams/2024/tenta-TATA54-20240822.pdf">TATA5420240822</a></td>
+<td class="org-left"><a href="exams/2024/tenta-TATA54-20240822-losning.pdf">TATA5420240822losn</a></td>
+</tr>
+
 <tr>
 <td class="org-right">2024-06-01</td>
 <td class="org-left">Jan Snellman</td>
@@ -1464,13 +1471,13 @@ De svenska versionerna är nyare. Några av föreläsningarna tar två tillfäll
 </section>
 
 
-<section id="outline-container-orgac41624" class="outline-2">
-<h2 id="orgac41624">Datorlaborationer <a id="org2d2cfa4"></a></h2>
-<div class="outline-text-2" id="text-orgac41624">
+<section id="outline-container-orgf236219" class="outline-2">
+<h2 id="orgf236219">Datorlaborationer <a id="org965b1f7"></a></h2>
+<div class="outline-text-2" id="text-orgf236219">
 </div>
-<div id="outline-container-orgd0ccf06" class="outline-3">
-<h3 id="orgd0ccf06">SageMath</h3>
-<div class="outline-text-3" id="text-orgd0ccf06">
+<div id="outline-container-org7a98c02" class="outline-3">
+<h3 id="org7a98c02">SageMath</h3>
+<div class="outline-text-3" id="text-org7a98c02">
 <p>
 Jag kommer att använda datoralgebraprogrammet <a href="https://www.sagemath.org/">SageMath</a> för att beräkna lite större exempel.
 Om ni vill experimentera på egen hand kan ni enkelt <a href="https://doc.sagemath.org/html/en/installation/index.html">installera programmet på er dator</a>,
@@ -1486,9 +1493,9 @@ Ett tredje alternativ, enkelt och flärdfritt, är att mata in sin kod till <a h
 </p>
 </div>
 </div>
-<div id="outline-container-orgd3b0180" class="outline-3">
-<h3 id="orgd3b0180">Kod från vissa föreläsningar</h3>
-<div class="outline-text-3" id="text-orgd3b0180">
+<div id="outline-container-org38724a4" class="outline-3">
+<h3 id="org38724a4">Kod från vissa föreläsningar</h3>
+<div class="outline-text-3" id="text-org38724a4">
 <ul class="org-ul">
 <li><a href="labs/lecture0.html">Föreläsning 0</a></li>
 <li><a href="labs/lecture1.html">Föreläsning 1</a></li>
@@ -1499,21 +1506,21 @@ Ett tredje alternativ, enkelt och flärdfritt, är att mata in sin kod till <a h
 </ul>
 </div>
 </div>
-<div id="outline-container-org85c34f4" class="outline-3">
-<h3 id="org85c34f4">Laborationer</h3>
-<div class="outline-text-3" id="text-org85c34f4">
+<div id="outline-container-org80ba8f8" class="outline-3">
+<h3 id="org80ba8f8">Laborationer</h3>
+<div class="outline-text-3" id="text-org80ba8f8">
 </div>
-<div id="outline-container-orga1be7da" class="outline-4">
-<h4 id="orga1be7da">Hensellyft, Primitiva rötter, Kinesiska restsatsen</h4>
-<div class="outline-text-4" id="text-orga1be7da">
+<div id="outline-container-org4bb0ea2" class="outline-4">
+<h4 id="org4bb0ea2">Hensellyft, Primitiva rötter, Kinesiska restsatsen</h4>
+<div class="outline-text-4" id="text-org4bb0ea2">
 <p>
 Finns att <a href="labs/HenselLyftLabHT2023.html">läsa direkt</a> eller som <a href="labs/HenselLyftLabHT2023.ipynb">Jupyter notebook</a> eller som <a href="labs/HenselLyftLabHT2023web.html">webapp</a>.
 </p>
 </div>
 </div>
-<div id="outline-container-org2528f16" class="outline-4">
-<h4 id="org2528f16">Kedjebråk</h4>
-<div class="outline-text-4" id="text-org2528f16">
+<div id="outline-container-org4f8b714" class="outline-4">
+<h4 id="org4f8b714">Kedjebråk</h4>
+<div class="outline-text-4" id="text-org4f8b714">
 <p>
 Finns att <a href="labs/kedjebraklab.html">läsa direkt</a> eller som <a href="labs/kedjebraklab.ipynb">Jupyter notebook</a> eller som <a href="labs/kedjebraklabweb.html">webapp</a>.
 </p>
@@ -1524,20 +1531,20 @@ Finns att <a href="labs/kedjebraklab.html">läsa direkt</a> eller som <a href="l
 
 
 
-<section id="outline-container-org27d49bb" class="outline-2">
-<h2 id="org27d49bb">Tidigare år <a id="orgb17e462"></a></h2>
-<div class="outline-text-2" id="text-org27d49bb">
+<section id="outline-container-org65b020a" class="outline-2">
+<h2 id="org65b020a">Tidigare år <a id="orgca3cfe8"></a></h2>
+<div class="outline-text-2" id="text-org65b020a">
 </div>
 
 
 
-<div id="outline-container-orga1fa650" class="outline-3">
-<h3 id="orga1fa650">TATA54 Anteckningar från tidigare år</h3>
-<div class="outline-text-3" id="text-orga1fa650">
+<div id="outline-container-org477262d" class="outline-3">
+<h3 id="org477262d">TATA54 Anteckningar från tidigare år</h3>
+<div class="outline-text-3" id="text-org477262d">
 </div>
-<div id="outline-container-orgd4aaf8a" class="outline-4">
-<h4 id="orgd4aaf8a">2023</h4>
-<div class="outline-text-4" id="text-orgd4aaf8a">
+<div id="outline-container-org780ed90" class="outline-4">
+<h4 id="org780ed90">2023</h4>
+<div class="outline-text-4" id="text-org780ed90">
 <ul class="org-ul">
 <li>2023-12-21: Gjorde klart <a href="index.html">denna nya kurshemsida</a>.</li>
 <li>2023-06-05: Jag har rättat tentan; en
@@ -1591,9 +1598,9 @@ tryckfel (skall vara w(d)). 7.2.38 är komplicerad och kan skippas.</li>
 </div>
 
 
-<div id="outline-container-orgc39991d" class="outline-4">
-<h4 id="orgc39991d">2021</h4>
-<div class="outline-text-4" id="text-orgc39991d">
+<div id="outline-container-org780092f" class="outline-4">
+<h4 id="org780092f">2021</h4>
+<div class="outline-text-4" id="text-org780092f">
 <ul class="org-ul">
 <li>2021-20-26: Alla klarade omtentan, trots att uppgift 5 kanske var
 oklar, jag menade periodLÄNGD för decimalutvecklingen, den kan
@@ -1641,9 +1648,9 @@ någon inbjudan, så mejla mig.</li>
 </div>
 </div>
 
-<div id="outline-container-org6bff760" class="outline-4">
-<h4 id="org6bff760">2020</h4>
-<div class="outline-text-4" id="text-org6bff760">
+<div id="outline-container-org2b03280" class="outline-4">
+<h4 id="org2b03280">2020</h4>
+<div class="outline-text-4" id="text-org2b03280">
 <ul class="org-ul">
 <li><p>
 2020-12-12: Kursen kommer att ges VT2021, med start den 19e januari.
@@ -1696,9 +1703,9 @@ someone else (perhaps
 </div>
 </div>
 
-<div id="outline-container-org85cd779" class="outline-4">
-<h4 id="org85cd779">2019</h4>
-<div class="outline-text-4" id="text-org85cd779">
+<div id="outline-container-org9b6101f" class="outline-4">
+<h4 id="org9b6101f">2019</h4>
+<div class="outline-text-4" id="text-org9b6101f">
 <ul class="org-ul">
 <li>2019-11-01: The course will not be given spring 2020.</li>
 
@@ -1713,9 +1720,9 @@ available.</li>
 </div>
 </div>
 
-<div id="outline-container-org21f5089" class="outline-4">
-<h4 id="org21f5089">2018</h4>
-<div class="outline-text-4" id="text-org21f5089">
+<div id="outline-container-orgba3d96f" class="outline-4">
+<h4 id="orgba3d96f">2018</h4>
+<div class="outline-text-4" id="text-orgba3d96f">
 <ul class="org-ul">
 <li>2018-06-08: <a href="exams/2018/tentaTATA5420180607soln.pdf">Solutions</a> to
 <a href="exams/2018/tenta20180607.pdf">the exam on June 7</a> are now
@@ -1728,9 +1735,9 @@ available.</li>
 </div>
 </div>
 
-<div id="outline-container-org7ce4987" class="outline-4">
-<h4 id="org7ce4987">2017</h4>
-<div class="outline-text-4" id="text-org7ce4987">
+<div id="outline-container-org45290d5" class="outline-4">
+<h4 id="org45290d5">2017</h4>
+<div class="outline-text-4" id="text-org45290d5">
 <ul class="org-ul">
 <li>2017-08-28: <a href="exams/2017/tentaTATA54170826soln.pdf">Solutions</a> to
 <a href="exams/2017/tenta170826.pdf">the exam on Saturday 26</a> are now
@@ -1753,7 +1760,7 @@ Another text is <a href="https://wstein.org/ent/">Elementary Number Theory</a> a
 </ul>
 
 
-<figure id="org2bc4bd6">
+<figure id="org73a3f81">
 <img src="img/sieveE.jpg" alt="sieveE.jpg">
 
 </figure>
@@ -1763,9 +1770,9 @@ Another text is <a href="https://wstein.org/ent/">Elementary Number Theory</a> a
 </section>
 
 
-<section id="outline-container-orga44ea53" class="outline-2">
-<h2 id="orga44ea53">Index</h2>
-<div class="outline-text-2" id="text-orga44ea53">
+<section id="outline-container-org22888c0" class="outline-2">
+<h2 id="org22888c0">Index</h2>
+<div class="outline-text-2" id="text-org22888c0">
 <p>
 <a href="sitemap.html">Samtliga nåbara filer</a>
 </p>
@@ -1774,7 +1781,7 @@ Another text is <a href="https://wstein.org/ent/">Elementary Number Theory</a> a
 </main>
 <footer id="postamble" class="status">
 <p class="author">F&ouml;rfattare: Jan Snellman Jan Snellman</p>
-<p class="date">Created: 2024-06-05</p>
+<p class="date">Created: 2024-08-22</p>
 <p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p>
 </footer>
 </body>
diff --git a/public/labs/HenselLyftLabHT2023.html b/public/labs/HenselLyftLabHT2023.html
index 4031be2aaad04e833493413665d219255f7877cb..d4fffeff6afdf9d33de3b960af6acd5658170983 100644
--- a/public/labs/HenselLyftLabHT2023.html
+++ b/public/labs/HenselLyftLabHT2023.html
@@ -1,7 +1,7 @@
 <!DOCTYPE html>
 <html lang="en">
 <head>
-<!-- 2024-04-05 -->
+<!-- 2024-08-22 -->
 <meta charset="utf-8" />
 <meta name="viewport" content="width=device-width, initial-scale=1" />
 <title>SageMath-övningar på Hensellyft, primitiva rötter, och KRS</title>
@@ -50,11 +50,11 @@
 <body>
 <header id="top" class="status">
 <div id="navbar" style ="text-align: center;">
-              <a href='https://liu.se'>LiU</a> -
-              <a href='https://liu.se/organisation/liu/mai'>MAI</a> -
-              <a href='https://liu.se/organisation/liu/mai'>Grundutbildning</a> -
-              <a href='https://courses.mai.liu.se/Lists/html/'>Kurser</a> -
-              <a href='index.html'>TATA54</a></div>
+                          <a href='https://liu.se'>LiU</a> -
+                          <a href='https://liu.se/organisation/liu/mai'>MAI</a> -
+                          <a href='https://liu.se/organisation/liu/mai'>Grundutbildning</a> -
+                          <a href='https://courses.mai.liu.se/Lists/html/'>Kurser</a> -
+                          <a href='index.html'>TATA54</a></div>
 </header>
 <main id="content" class="content">
 <header>
@@ -65,22 +65,22 @@
 <ul>
 <li><a href="#unika-hensellyft">Ej unika hensellyft</a>
 <ul>
-<li><a href="#orgb923ff8">Exempel 1, unika lyft</a>
+<li><a href="#orgd387462">Exempel 1, unika lyft</a>
 <ul>
-<li><a href="#org6be1fa2">Övning 1</a></li>
-<li><a href="#orgc35d91f">Större p, fortfarande unika lyft</a></li>
-<li><a href="#orgd3c72b3">Övning 2</a></li>
+<li><a href="#org553e3fc">Övning 1</a></li>
+<li><a href="#orgf02802e">Större p, fortfarande unika lyft</a></li>
+<li><a href="#org6242051">Övning 2</a></li>
 </ul>
 </li>
 </ul>
 </li>
-<li><a href="#org659b2ca">Unika lyft</a>
+<li><a href="#org104f746">Unika lyft</a>
 <ul>
 <li><a href="#exempel-4.21">Exempel 4.21</a></li>
-<li><a href="#org632696a">övning 3</a></li>
+<li><a href="#org1868400">övning 3</a></li>
 <li><a href="#ex-4.23">Ex 4.23</a>
 <ul>
-<li><a href="#org59ffa70">Övning 4</a></li>
+<li><a href="#orgb19d4b7">Övning 4</a></li>
 </ul>
 </li>
 </ul>
@@ -89,11 +89,11 @@
 <ul>
 <li><a href="#ex-4.22">Ex 4.22</a>
 <ul>
-<li><a href="#orgd02384a">Övning 5</a></li>
-<li><a href="#org7f5a24e">Övning 6</a></li>
+<li><a href="#org9fa80b2">Övning 5</a></li>
+<li><a href="#org9dff539">Övning 6</a></li>
 </ul>
 </li>
-<li><a href="#org1b1b5b2">Allt lyfter inte</a></li>
+<li><a href="#orgde4c67d">Allt lyfter inte</a></li>
 </ul>
 </li>
 <li><a href="#kvadratrötter-mm">Kvadratrötter mm</a>
@@ -113,7 +113,7 @@
 </div>
 </nav>
 <div class="org-src-container">
-<pre class="src src-sage" id="org8903563">def H_L_tree(f, p: int, r: int):
+<pre class="src src-sage" id="org750e867">def H_L_tree(f, p: int, r: int):
 
     vert = [(0,0)]
     for j in range(1,r+1):
@@ -136,9 +136,9 @@
 <div class="outline-text-2" id="text-unika-hensellyft">
 </div>
 
-<div id="outline-container-orgb923ff8" class="outline-3">
-<h3 id="orgb923ff8">Exempel 1, unika lyft</h3>
-<div class="outline-text-3" id="text-orgb923ff8">
+<div id="outline-container-orgd387462" class="outline-3">
+<h3 id="orgd387462">Exempel 1, unika lyft</h3>
+<div class="outline-text-3" id="text-orgd387462">
 <p>
 \(x^{^{p-1}} -1 \mod p^r\)
 </p>
@@ -160,7 +160,7 @@ H_L_tree(f,p,r).plot(layout='tree')
 </div>
 
 
-<figure id="org6aac4a1">
+<figure id="orgab9b3e3">
 <img src="../img/HenselLyftLabHT2023_fig1.png" alt="HenselLyftLabHT2023_fig1.png">
 
 </figure>
@@ -180,7 +180,7 @@ H_L_tree(f,p,r).plot(layout='tree')
 </div>
 
 
-<figure id="org97d4a85">
+<figure id="orgf3bbcb5">
 <img src="../img/HenselLyftLabHT2023_fig1.png" alt="HenselLyftLabHT2023_fig1.png">
 
 </figure>
@@ -197,7 +197,7 @@ H_L_tree(f,p,r).plot(layout='tree')
 </div>
 
 
-<figure id="orgadb1bc0">
+<figure id="org747f18f">
 <img src="../img/HenselLyftLabHT2023_fig1.png" alt="HenselLyftLabHT2023_fig1.png">
 
 </figure>
@@ -213,7 +213,7 @@ H_L_tree(f,p,r).plot(layout='tree')
 </div>
 
 
-<figure id="orgee6db14">
+<figure id="org02252c4">
 <img src="../img/HenselLyftLabHT2023_fig1.png" alt="HenselLyftLabHT2023_fig1.png">
 
 </figure>
@@ -287,9 +287,9 @@ y
 </div>
 </div>
 
-<div id="outline-container-org6be1fa2" class="outline-4">
-<h4 id="org6be1fa2">Övning 1</h4>
-<div class="outline-text-4" id="text-org6be1fa2">
+<div id="outline-container-org553e3fc" class="outline-4">
+<h4 id="org553e3fc">Övning 1</h4>
+<div class="outline-text-4" id="text-org553e3fc">
 <p>
 Välj en tredje rot och lyft den
 </p>
@@ -298,9 +298,9 @@ Välj en tredje rot och lyft den
 
 
 
-<div id="outline-container-orgc35d91f" class="outline-4">
-<h4 id="orgc35d91f">Större p, fortfarande unika lyft</h4>
-<div class="outline-text-4" id="text-orgc35d91f">
+<div id="outline-container-orgf02802e" class="outline-4">
+<h4 id="orgf02802e">Större p, fortfarande unika lyft</h4>
+<div class="outline-text-4" id="text-orgf02802e">
 <p>
 Hitta nollställena mod p<sup>n</sup> till följande:
 </p>
@@ -316,7 +316,7 @@ H_L_tree(f,p,r).plot(layout='tree')
 </div>
 
 
-<figure id="orgfe5b92a">
+<figure id="org86d33c9">
 <img src="../img/HenselLyftLabHT2023_fig2.png" alt="HenselLyftLabHT2023_fig2.png">
 
 </figure>
@@ -325,9 +325,9 @@ H_L_tree(f,p,r).plot(layout='tree')
 
 
 
-<div id="outline-container-orgd3c72b3" class="outline-4">
-<h4 id="orgd3c72b3">Övning 2</h4>
-<div class="outline-text-4" id="text-orgd3c72b3">
+<div id="outline-container-org6242051" class="outline-4">
+<h4 id="org6242051">Övning 2</h4>
+<div class="outline-text-4" id="text-org6242051">
 <p>
 Har f några rationella rötter? (Ignorera bilden, gör en egen utredning).
 Välj någon rot mod p och lyft den.
@@ -338,9 +338,9 @@ Välj någon rot mod p och lyft den.
 </section>
 
 
-<section id="outline-container-org659b2ca" class="outline-2">
-<h2 id="org659b2ca">Unika lyft</h2>
-<div class="outline-text-2" id="text-org659b2ca">
+<section id="outline-container-org104f746" class="outline-2">
+<h2 id="org104f746">Unika lyft</h2>
+<div class="outline-text-2" id="text-org104f746">
 </div>
 <div id="outline-container-exempel-4.21" class="outline-3">
 <h3 id="exempel-4.21">Exempel 4.21</h3>
@@ -359,7 +359,7 @@ f = R(x^3 + x^2 + 29)
 </div>
 
 
-<figure id="org7058de8">
+<figure id="org37c700b">
 <img src="../img/HenselLyftLabHT2023_fig3.png" alt="HenselLyftLabHT2023_fig3.png">
 
 </figure>
@@ -424,9 +424,9 @@ fq, fq.hensel_lift(p,3)
 </div>
 
 
-<div id="outline-container-org632696a" class="outline-3">
-<h3 id="org632696a">övning 3</h3>
-<div class="outline-text-3" id="text-org632696a">
+<div id="outline-container-org1868400" class="outline-3">
+<h3 id="org1868400">övning 3</h3>
+<div class="outline-text-3" id="text-org1868400">
 <p>
 Lyft ännu högre, jämför båda metoderna
 </p>
@@ -450,15 +450,15 @@ f = x^3 + x^2 +2*x + 26
 </div>
 
 
-<figure id="org1cc7864">
+<figure id="orgf426430">
 <img src="../img/HenselLyftLabHT2023_fig4.png" alt="HenselLyftLabHT2023_fig4.png">
 
 </figure>
 </div>
 
-<div id="outline-container-org59ffa70" class="outline-4">
-<h4 id="org59ffa70">Övning 4</h4>
-<div class="outline-text-4" id="text-org59ffa70">
+<div id="outline-container-orgb19d4b7" class="outline-4">
+<h4 id="orgb19d4b7">Övning 4</h4>
+<div class="outline-text-4" id="text-orgb19d4b7">
 <p>
 Gör de unika lyften via Hensel!
 </p>
@@ -487,15 +487,15 @@ f = x^2 + x + 7
 </div>
 
 
-<figure id="orge5ad7dd">
+<figure id="org8dd820b">
 <img src="../img/HenselLyftLabHT2023_fig5.png" alt="HenselLyftLabHT2023_fig5.png">
 
 </figure>
 </div>
 
-<div id="outline-container-orgd02384a" class="outline-4">
-<h4 id="orgd02384a">Övning 5</h4>
-<div class="outline-text-4" id="text-orgd02384a">
+<div id="outline-container-org9fa80b2" class="outline-4">
+<h4 id="org9fa80b2">Övning 5</h4>
+<div class="outline-text-4" id="text-org9fa80b2">
 <p>
 Så finns lösningar upp till mod \(p^3\) men ej mod \(p^4\), varför?
 Red ut detta, ledning nedan
@@ -540,9 +540,9 @@ För vart och ett av dessa så är antingen alla eller inga av dess lyft nollst
 </div>
 
 
-<div id="outline-container-org7f5a24e" class="outline-4">
-<h4 id="org7f5a24e">Övning 6</h4>
-<div class="outline-text-4" id="text-org7f5a24e">
+<div id="outline-container-org9dff539" class="outline-4">
+<h4 id="org9dff539">Övning 6</h4>
+<div class="outline-text-4" id="text-org9dff539">
 <p>
 Finns det polynom med icke-unika lyft som trots allt har nollställen mod \(p^n\) alla n, som
 inte kommer från rationella nollställen?
@@ -553,9 +553,9 @@ inte kommer från rationella nollställen?
 
 
 
-<div id="outline-container-org1b1b5b2" class="outline-3">
-<h3 id="org1b1b5b2">Allt lyfter inte</h3>
-<div class="outline-text-3" id="text-org1b1b5b2">
+<div id="outline-container-orgde4c67d" class="outline-3">
+<h3 id="orgde4c67d">Allt lyfter inte</h3>
+<div class="outline-text-3" id="text-orgde4c67d">
 <p>
 Ex: den rationella roten -1 är den enda som lyfter mot oändligheten
 </p>
@@ -571,7 +571,7 @@ H_L_tree(f,p,r).plot(layout='tree')
 </div>
 
 
-<figure id="org64a6106">
+<figure id="org0fc508c">
 <img src="../img/HenselLyftLabHT2023_fig6.png" alt="HenselLyftLabHT2023_fig6.png">
 
 </figure>
@@ -592,8 +592,8 @@ som lyfter icke-unikt mot evigheten?
 
 
 <ul class="org-ul">
-<li><a id="orgf69f4c9"></a>Ledning nedan om du kör fast<br>
-<div class="outline-text-5" id="text-orgf69f4c9">
+<li><a id="orga4baaa3"></a>Ledning nedan om du kör fast<br>
+<div class="outline-text-5" id="text-orga4baaa3">
 <p>
 försök med
 \(p=2\) och
@@ -715,7 +715,7 @@ f = x^2 -3
 </div>
 
 
-<figure id="orgd7e68e1">
+<figure id="orge682744">
 <img src="../img/HenselLyftLabHT2023_fig21.png" alt="HenselLyftLabHT2023_fig21.png">
 
 </figure>
@@ -1092,7 +1092,7 @@ f = R(x^3 + x^2 + 29)
 </div>
 
 
-<figure id="orgac5479f">
+<figure id="org46df024">
 <img src="../img/HenselLyftLabHT2023_fig31.png" alt="HenselLyftLabHT2023_fig31.png">
 
 </figure>
@@ -1103,7 +1103,7 @@ f = R(x^3 + x^2 + 29)
 </div>
 
 
-<figure id="orgf54282b">
+<figure id="orgfe1eb75">
 <img src="../img/HenselLyftLabHT2023_fig33.png" alt="HenselLyftLabHT2023_fig33.png">
 
 </figure>
@@ -1114,7 +1114,7 @@ f = R(x^3 + x^2 + 29)
 </div>
 
 
-<figure id="orgefb2d91">
+<figure id="orga92116c">
 <img src="../img/HenselLyftLabHT2023_fig35.png" alt="HenselLyftLabHT2023_fig35.png">
 
 </figure>
@@ -1142,7 +1142,7 @@ f = R(x^3 + x^2 + 29)
 </main>
 <footer id="postamble" class="status">
 <p class="author">Author: Jan Snellman</p>
-<p class="date">Created: 2024-04-05</p>
+<p class="date">Created: 2024-08-22</p>
 <p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p>
 </footer>
 </body>
diff --git a/public/labs/kedjebraklab.html b/public/labs/kedjebraklab.html
index c20ccf340a367290bff5e6ba2813c9ab3f507dee..c78d888c3b003b0da087cfcc9e9b4ba5757a79af 100644
--- a/public/labs/kedjebraklab.html
+++ b/public/labs/kedjebraklab.html
@@ -1,7 +1,7 @@
 <!DOCTYPE html>
 <html lang="en">
 <head>
-<!-- 2024-01-12 -->
+<!-- 2024-08-22 -->
 <meta charset="utf-8" />
 <meta name="viewport" content="width=device-width, initial-scale=1" />
 <title>Sagemath-övningar på kedjebråk</title>
@@ -196,11 +196,11 @@
 <body>
 <header id="top" class="status">
 <div id="navbar" style ="text-align: center;">
-              <a href='https://liu.se'>LiU</a> -
-              <a href='https://liu.se/organisation/liu/mai'>MAI</a> -
-              <a href='https://liu.se/organisation/liu/mai'>Grundutbildning</a> -
-              <a href='https://courses.mai.liu.se/Lists/html/'>Kurser</a> -
-              <a href='index.html'>TATA54</a></div>
+                          <a href='https://liu.se'>LiU</a> -
+                          <a href='https://liu.se/organisation/liu/mai'>MAI</a> -
+                          <a href='https://liu.se/organisation/liu/mai'>Grundutbildning</a> -
+                          <a href='https://courses.mai.liu.se/Lists/html/'>Kurser</a> -
+                          <a href='index.html'>TATA54</a></div>
 </header>
 <main id="content" class="content">
 <header>
@@ -259,7 +259,7 @@ kb1
 </div>
 
 
-<figure id="org370e5f5">
+<figure id="org52de908">
 <img src="img/kedjebraklab_fig_1.png" alt="kedjebraklab_fig_1.png">
 
 </figure>
@@ -396,8 +396,8 @@ ut
 </main>
 <footer id="postamble" class="status">
 <p class="author">Author: Jan Snellman</p>
-<p class="date">Created: 2024-01-12</p>
+<p class="date">Created: 2024-08-22</p>
 <p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p>
 </footer>
 </body>
-</html>
\ No newline at end of file
+</html>
diff --git a/public/labs/lecture0.html b/public/labs/lecture0.html
index 09ae0d686fda4a3ebbb802893ca69f4cd0cd6e16..271658af0f2b154685a54e5b4f9463b68b534680 100644
--- a/public/labs/lecture0.html
+++ b/public/labs/lecture0.html
@@ -1,7 +1,7 @@
 <!DOCTYPE html>
 <html lang="en">
 <head>
-<!-- 2024-01-12 -->
+<!-- 2024-08-22 -->
 <meta charset="utf-8" />
 <meta name="viewport" content="width=device-width, initial-scale=1" />
 <title>&lrm;</title>
@@ -196,11 +196,11 @@
 <body>
 <header id="top" class="status">
 <div id="navbar" style ="text-align: center;">
-              <a href='https://liu.se'>LiU</a> -
-              <a href='https://liu.se/organisation/liu/mai'>MAI</a> -
-              <a href='https://liu.se/organisation/liu/mai'>Grundutbildning</a> -
-              <a href='https://courses.mai.liu.se/Lists/html/'>Kurser</a> -
-              <a href='index.html'>TATA54</a></div>
+                          <a href='https://liu.se'>LiU</a> -
+                          <a href='https://liu.se/organisation/liu/mai'>MAI</a> -
+                          <a href='https://liu.se/organisation/liu/mai'>Grundutbildning</a> -
+                          <a href='https://courses.mai.liu.se/Lists/html/'>Kurser</a> -
+                          <a href='index.html'>TATA54</a></div>
 </header>
 <main id="content" class="content">
 <div class="org-src-container">
@@ -212,7 +212,7 @@ plot([prime_pi(x),x/ln(x)],(1,100))
 </div>
 
 
-<figure id="org9dde164">
+<figure id="orgfedf573">
 <img src="file:///tmp/tmpob0hnw37/tmp_zm_txld0.png" alt="tmp_zm_txld0.png">
 
 </figure>
@@ -227,7 +227,7 @@ plot([prime_pi(x)/x]+FL,(100,1000))
 </div>
 
 
-<figure id="org666e17f">
+<figure id="org8e7e000">
 <img src="file:///tmp/tmpob0hnw37/tmp_a0i_rmcl.png" alt="tmp_a0i_rmcl.png">
 
 </figure>
@@ -254,7 +254,7 @@ for L in P5:
 </pre>
 </div>
 
-<pre class="example" id="org840d8c5">
+<pre class="example" id="org4624854">
 [5]
 *****
 [4, 1]
@@ -290,15 +290,15 @@ for L in P5:
 </div>
 
 
-<figure id="org28cf4cd">
+<figure id="org8c50c08">
 <img src="file:///tmp/tmpob0hnw37/tmp_40jucrn2.png" alt="tmp_40jucrn2.png">
 
 </figure>
 </main>
 <footer id="postamble" class="status">
 <p class="author">Author: Jan Snellman</p>
-<p class="date">Created: 2024-01-12</p>
+<p class="date">Created: 2024-08-22</p>
 <p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p>
 </footer>
 </body>
-</html>
\ No newline at end of file
+</html>
diff --git a/public/labs/lecture1.html b/public/labs/lecture1.html
index 2a407cbdbd194cee28122153733737ec07c11900..7b758efb08a1619d9fb06031f797b0bace1bc18d 100644
--- a/public/labs/lecture1.html
+++ b/public/labs/lecture1.html
@@ -1,7 +1,7 @@
 <!DOCTYPE html>
 <html lang="en">
 <head>
-<!-- 2024-01-12 -->
+<!-- 2024-08-22 -->
 <meta charset="utf-8" />
 <meta name="viewport" content="width=device-width, initial-scale=1" />
 <title>&lrm;</title>
@@ -196,11 +196,11 @@
 <body>
 <header id="top" class="status">
 <div id="navbar" style ="text-align: center;">
-              <a href='https://liu.se'>LiU</a> -
-              <a href='https://liu.se/organisation/liu/mai'>MAI</a> -
-              <a href='https://liu.se/organisation/liu/mai'>Grundutbildning</a> -
-              <a href='https://courses.mai.liu.se/Lists/html/'>Kurser</a> -
-              <a href='index.html'>TATA54</a></div>
+                          <a href='https://liu.se'>LiU</a> -
+                          <a href='https://liu.se/organisation/liu/mai'>MAI</a> -
+                          <a href='https://liu.se/organisation/liu/mai'>Grundutbildning</a> -
+                          <a href='https://courses.mai.liu.se/Lists/html/'>Kurser</a> -
+                          <a href='index.html'>TATA54</a></div>
 </header>
 <main id="content" class="content">
 <div class="org-src-container">
@@ -210,7 +210,7 @@ Q.plot()
 </div>
 
 
-<figure id="org14e4735">
+<figure id="org0cb5663">
 <img src="9ac1a989740cf989527eb8832af86aed4687c15c.png" alt="9ac1a989740cf989527eb8832af86aed4687c15c.png">
 
 </figure>
@@ -222,7 +222,7 @@ W.plot()
 </div>
 
 
-<figure id="orga853ba9">
+<figure id="org19bc0a2">
 <img src="fefcb50303c1aece74eb2f07e81f7dcba64c9305.png" alt="fefcb50303c1aece74eb2f07e81f7dcba64c9305.png">
 
 </figure>
@@ -244,7 +244,7 @@ W.plot()
 </pre>
 </div>
 
-<pre class="example" id="org21704c4">
+<pre class="example" id="org893ac51">
 ---------------------------------------------------------------------------
 TypeError                                 Traceback (most recent call last)
 &lt;ipython-input-8-58a5f6bfd37d&gt; in &lt;module&gt;()
@@ -262,7 +262,7 @@ TypeError: gcd() takes at most 2 arguments (3 given)
 </pre>
 </div>
 
-<pre class="example" id="org610cede">
+<pre class="example" id="org3296028">
 Object `diophantine` not found.
 </pre>
 
@@ -281,7 +281,7 @@ Object `diophantine` not found.
 </div>
 
 
-<figure id="org777c8dd">
+<figure id="org2407621">
 <img src="326e354523c67057c4312517686106179ab4db51.png" alt="326e354523c67057c4312517686106179ab4db51.png">
 
 </figure>
@@ -293,8 +293,8 @@ Object `diophantine` not found.
 </main>
 <footer id="postamble" class="status">
 <p class="author">Author: Jan Snellman</p>
-<p class="date">Created: 2024-01-12</p>
+<p class="date">Created: 2024-08-22</p>
 <p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p>
 </footer>
 </body>
-</html>
\ No newline at end of file
+</html>
diff --git a/public/labs/lecture2.html b/public/labs/lecture2.html
index 31c825e179737d21168a187f1a838560ef32f7a0..eab766bdc1cba17bdf5d7a80f75e9b405daac1dc 100644
--- a/public/labs/lecture2.html
+++ b/public/labs/lecture2.html
@@ -1,7 +1,7 @@
 <!DOCTYPE html>
 <html lang="en">
 <head>
-<!-- 2024-01-12 -->
+<!-- 2024-08-22 -->
 <meta charset="utf-8" />
 <meta name="viewport" content="width=device-width, initial-scale=1" />
 <title>&lrm;</title>
@@ -196,11 +196,11 @@
 <body>
 <header id="top" class="status">
 <div id="navbar" style ="text-align: center;">
-              <a href='https://liu.se'>LiU</a> -
-              <a href='https://liu.se/organisation/liu/mai'>MAI</a> -
-              <a href='https://liu.se/organisation/liu/mai'>Grundutbildning</a> -
-              <a href='https://courses.mai.liu.se/Lists/html/'>Kurser</a> -
-              <a href='index.html'>TATA54</a></div>
+                          <a href='https://liu.se'>LiU</a> -
+                          <a href='https://liu.se/organisation/liu/mai'>MAI</a> -
+                          <a href='https://liu.se/organisation/liu/mai'>Grundutbildning</a> -
+                          <a href='https://courses.mai.liu.se/Lists/html/'>Kurser</a> -
+                          <a href='index.html'>TATA54</a></div>
 </header>
 <main id="content" class="content">
 <div class="org-src-container">
@@ -217,7 +217,7 @@ P8 =  point([(6+3*cos(2*pi*4/15),3*sin(2*pi*4/15))],  color='green',size=30)
 </div>
 
 
-<figure id="orge57e015">
+<figure id="org51df67d">
 <img src="c67ffb39f62f2392dfa28b6784c3c3d3bcd05ee8.png" alt="c67ffb39f62f2392dfa28b6784c3c3d3bcd05ee8.png">
 
 </figure>
@@ -283,7 +283,7 @@ Cyclic4
 </div>
 
 
-<figure id="org2291500">
+<figure id="org4ef1e24">
 <img src="baac293abd935204538782ac3c46dafecc9de285.png" alt="baac293abd935204538782ac3c46dafecc9de285.png">
 
 </figure>
@@ -294,7 +294,7 @@ Cyclic4
 </div>
 
 
-<figure id="org1d4e4cd">
+<figure id="org4c7626a">
 <img src="c0e9ecb85854981cf29210e7cd25e81d382aa9b3.png" alt="c0e9ecb85854981cf29210e7cd25e81d382aa9b3.png">
 
 </figure>
@@ -314,7 +314,7 @@ Cyclic4
 </pre>
 </div>
 
-<pre class="example" id="org721ef33">
+<pre class="example" id="org3eeb40e">
 1
 2
 2
@@ -331,7 +331,7 @@ Cyclic4
 </div>
 
 
-<figure id="org1178560">
+<figure id="org3a1f8ae">
 <img src="79b2d76d2217581bc5e8ff8caf581a6d3bfcc9ad.png" alt="79b2d76d2217581bc5e8ff8caf581a6d3bfcc9ad.png">
 
 </figure>
@@ -343,8 +343,8 @@ Cyclic4
 </main>
 <footer id="postamble" class="status">
 <p class="author">Author: Jan Snellman</p>
-<p class="date">Created: 2024-01-12</p>
+<p class="date">Created: 2024-08-22</p>
 <p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p>
 </footer>
 </body>
-</html>
\ No newline at end of file
+</html>
diff --git a/public/labs/lecture3.html b/public/labs/lecture3.html
index 26327ea63b2294df175c8ed8d6d9b4a5c532b247..f7a31dfa79531e38bfba24eb271617cf698addf4 100644
--- a/public/labs/lecture3.html
+++ b/public/labs/lecture3.html
@@ -1,7 +1,7 @@
 <!DOCTYPE html>
 <html lang="en">
 <head>
-<!-- 2024-01-12 -->
+<!-- 2024-08-22 -->
 <meta charset="utf-8" />
 <meta name="viewport" content="width=device-width, initial-scale=1" />
 <title>&lrm;</title>
@@ -196,11 +196,11 @@
 <body>
 <header id="top" class="status">
 <div id="navbar" style ="text-align: center;">
-              <a href='https://liu.se'>LiU</a> -
-              <a href='https://liu.se/organisation/liu/mai'>MAI</a> -
-              <a href='https://liu.se/organisation/liu/mai'>Grundutbildning</a> -
-              <a href='https://courses.mai.liu.se/Lists/html/'>Kurser</a> -
-              <a href='index.html'>TATA54</a></div>
+                          <a href='https://liu.se'>LiU</a> -
+                          <a href='https://liu.se/organisation/liu/mai'>MAI</a> -
+                          <a href='https://liu.se/organisation/liu/mai'>Grundutbildning</a> -
+                          <a href='https://courses.mai.liu.se/Lists/html/'>Kurser</a> -
+                          <a href='index.html'>TATA54</a></div>
 </header>
 <main id="content" class="content">
 <div class="org-src-container">
@@ -209,7 +209,7 @@
 </div>
 
 
-<figure id="orge200e74">
+<figure id="org140733c">
 <img src="eec132b7c338bf28fddfea6ec0238fd154197cd1.png" alt="eec132b7c338bf28fddfea6ec0238fd154197cd1.png">
 
 </figure>
@@ -222,7 +222,7 @@ DN.show()
 </div>
 
 
-<figure id="org3ee5e13">
+<figure id="org909ae18">
 <img src="f23f2c41ea39457fc3c9bf916511610731f1daf2.png" alt="f23f2c41ea39457fc3c9bf916511610731f1daf2.png">
 
 </figure>
@@ -259,7 +259,7 @@ L.plot(vertex_colors=H,pos=mypos)
 </div>
 
 
-<figure id="orgf75fa7b">
+<figure id="org6572d27">
 <img src="3de4085389dcddfbf10a5a83509b5920afc0c3ce.png" alt="3de4085389dcddfbf10a5a83509b5920afc0c3ce.png">
 
 </figure>
@@ -273,7 +273,7 @@ eul+ep
 </div>
 
 
-<figure id="org7112945">
+<figure id="org8b45232">
 <img src="1118cc771effff59b550fa536c0cfb54e17ab5d2.png" alt="1118cc771effff59b550fa536c0cfb54e17ab5d2.png">
 
 </figure>
@@ -285,8 +285,8 @@ eul+ep
 </main>
 <footer id="postamble" class="status">
 <p class="author">Author: Jan Snellman</p>
-<p class="date">Created: 2024-01-12</p>
+<p class="date">Created: 2024-08-22</p>
 <p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p>
 </footer>
 </body>
-</html>
\ No newline at end of file
+</html>
diff --git a/public/labs/lecture4.html b/public/labs/lecture4.html
index 4c806c809f1745eef5e6c6fdfff686cdee07f250..d61f0df62ef74a33f2004c2058cfa85730c65972 100644
--- a/public/labs/lecture4.html
+++ b/public/labs/lecture4.html
@@ -1,7 +1,7 @@
 <!DOCTYPE html>
 <html lang="en">
 <head>
-<!-- 2024-01-12 -->
+<!-- 2024-08-22 -->
 <meta charset="utf-8" />
 <meta name="viewport" content="width=device-width, initial-scale=1" />
 <title>&lrm;</title>
@@ -196,11 +196,11 @@
 <body>
 <header id="top" class="status">
 <div id="navbar" style ="text-align: center;">
-              <a href='https://liu.se'>LiU</a> -
-              <a href='https://liu.se/organisation/liu/mai'>MAI</a> -
-              <a href='https://liu.se/organisation/liu/mai'>Grundutbildning</a> -
-              <a href='https://courses.mai.liu.se/Lists/html/'>Kurser</a> -
-              <a href='index.html'>TATA54</a></div>
+                          <a href='https://liu.se'>LiU</a> -
+                          <a href='https://liu.se/organisation/liu/mai'>MAI</a> -
+                          <a href='https://liu.se/organisation/liu/mai'>Grundutbildning</a> -
+                          <a href='https://courses.mai.liu.se/Lists/html/'>Kurser</a> -
+                          <a href='index.html'>TATA54</a></div>
 </header>
 <main id="content" class="content">
 <div class="org-src-container">
@@ -286,8 +286,8 @@ ff
 </main>
 <footer id="postamble" class="status">
 <p class="author">Author: Jan Snellman</p>
-<p class="date">Created: 2024-01-12</p>
+<p class="date">Created: 2024-08-22</p>
 <p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p>
 </footer>
 </body>
-</html>
\ No newline at end of file
+</html>
diff --git a/public/labs/lecture5.html b/public/labs/lecture5.html
index f275e964e4bc84d7e052781b8693ef78a3ee7d31..cca5d282af73f604a54b321db2f8d45738de7f5f 100644
--- a/public/labs/lecture5.html
+++ b/public/labs/lecture5.html
@@ -1,7 +1,7 @@
 <!DOCTYPE html>
 <html lang="en">
 <head>
-<!-- 2024-01-12 -->
+<!-- 2024-08-22 -->
 <meta charset="utf-8" />
 <meta name="viewport" content="width=device-width, initial-scale=1" />
 <title>&lrm;</title>
@@ -196,11 +196,11 @@
 <body>
 <header id="top" class="status">
 <div id="navbar" style ="text-align: center;">
-              <a href='https://liu.se'>LiU</a> -
-              <a href='https://liu.se/organisation/liu/mai'>MAI</a> -
-              <a href='https://liu.se/organisation/liu/mai'>Grundutbildning</a> -
-              <a href='https://courses.mai.liu.se/Lists/html/'>Kurser</a> -
-              <a href='index.html'>TATA54</a></div>
+                          <a href='https://liu.se'>LiU</a> -
+                          <a href='https://liu.se/organisation/liu/mai'>MAI</a> -
+                          <a href='https://liu.se/organisation/liu/mai'>Grundutbildning</a> -
+                          <a href='https://courses.mai.liu.se/Lists/html/'>Kurser</a> -
+                          <a href='index.html'>TATA54</a></div>
 </header>
 <main id="content" class="content">
 <div class="org-src-container">
@@ -209,7 +209,7 @@ print p
 </pre>
 </div>
 
-<pre class="example" id="orge2fd40e">
+<pre class="example" id="orgf8a44a9">
 2441
 </pre>
 
@@ -219,7 +219,7 @@ print(myfact)
 </pre>
 </div>
 
-<pre class="example" id="orgbde3826">
+<pre class="example" id="org0f9e188">
 2^3 * 5 * 61
 </pre>
 
@@ -242,7 +242,7 @@ for fact in myfact:
 </pre>
 </div>
 
-<pre class="example" id="org01dd320">
+<pre class="example" id="orgf2f4ac7">
 x^4 + 2440 x^8 + 2440 {672, 1, 1122, 1319, 2440, 1769, 2156, 285} {2440, 1769, 672, 1} 1122
 x + 2440 x^5 + 2440 {1, 583, 1478, 590, 2230} {1} 1478
 x + 2440 x^61 + 2440 {1280, 1024, 1283, 1029, 1, 1547, 268, 1421, 1166, 1679, 1040, 1002, 2067, 1300, 534, 26, 261, 32, 676, 2086, 1832, 1195, 684, 2290, 50, 40, 2104, 697, 59, 956, 189, 446, 2214, 832, 1035, 331, 2380, 845, 2157, 2127, 2000, 1600, 855, 1625, 335, 2360, 1888, 739, 1253, 103, 828, 1642, 1387, 237, 1904, 753, 1778, 489, 509, 1534, 2344} {1} 1280
@@ -254,7 +254,7 @@ print multiplicative_order(c)
 </pre>
 </div>
 
-<pre class="example" id="org27f5926">
+<pre class="example" id="org5645c51">
 {1280, 1122, 1478} 2141
 2440
 </pre>
@@ -283,8 +283,8 @@ thelifts
 </main>
 <footer id="postamble" class="status">
 <p class="author">Author: Jan Snellman</p>
-<p class="date">Created: 2024-01-12</p>
+<p class="date">Created: 2024-08-22</p>
 <p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p>
 </footer>
 </body>
-</html>
\ No newline at end of file
+</html>
diff --git a/public/lectures/Henselfaktorisering.html b/public/lectures/Henselfaktorisering.html
index 0d2f47a3df095b7c99f43fa08f8debcc050ddd1c..52ff66746252f6f7af317c2d7f85a4b89ccb57a8 100644
--- a/public/lectures/Henselfaktorisering.html
+++ b/public/lectures/Henselfaktorisering.html
@@ -1,7 +1,7 @@
 <!DOCTYPE html>
 <html lang="en">
 <head>
-<!-- 2024-01-12 -->
+<!-- 2024-08-22 -->
 <meta charset="utf-8" />
 <meta name="viewport" content="width=device-width, initial-scale=1" />
 <title>Henselfaktorisering</title>
@@ -196,19 +196,19 @@
 <body>
 <header id="top" class="status">
 <div id="navbar" style ="text-align: center;">
-              <a href='https://liu.se'>LiU</a> -
-              <a href='https://liu.se/organisation/liu/mai'>MAI</a> -
-              <a href='https://liu.se/organisation/liu/mai'>Grundutbildning</a> -
-              <a href='https://courses.mai.liu.se/Lists/html/'>Kurser</a> -
-              <a href='index.html'>TATA54</a></div>
+                          <a href='https://liu.se'>LiU</a> -
+                          <a href='https://liu.se/organisation/liu/mai'>MAI</a> -
+                          <a href='https://liu.se/organisation/liu/mai'>Grundutbildning</a> -
+                          <a href='https://courses.mai.liu.se/Lists/html/'>Kurser</a> -
+                          <a href='index.html'>TATA54</a></div>
 </header>
 <main id="content" class="content">
 <header>
 <h1 class="title">Henselfaktorisering</h1>
 </header>
-<section id="outline-container-orgdb8e25d" class="outline-2">
-<h2 id="orgdb8e25d">Faktorisering via Hensel</h2>
-<div class="outline-text-2" id="text-orgdb8e25d">
+<section id="outline-container-orge485e39" class="outline-2">
+<h2 id="orge485e39">Faktorisering via Hensel</h2>
+<div class="outline-text-2" id="text-orge485e39">
 <p>
 <img src="../img/faktorhensel-1.png" alt="faktorhensel-1.png">
 <img src="../img/faktorhensel-2.png" alt="faktorhensel-2.png">
@@ -221,8 +221,8 @@
 </main>
 <footer id="postamble" class="status">
 <p class="author">Author: Jan Snellman</p>
-<p class="date">Created: 2024-01-12</p>
+<p class="date">Created: 2024-08-22</p>
 <p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p>
 </footer>
 </body>
-</html>
\ No newline at end of file
+</html>
diff --git a/public/newlectures/new-lect-0.html b/public/newlectures/new-lect-0.html
index feebd46ed01ade411aec2768801655a11a8e8809..46acbc60458254cda40a8874f8176e14df3709b8 100644
--- a/public/newlectures/new-lect-0.html
+++ b/public/newlectures/new-lect-0.html
@@ -1,7 +1,7 @@
 <!DOCTYPE html>
 <html lang="sv">
 <head>
-<!-- 2024-02-06 -->
+<!-- 2024-08-22 -->
 <meta charset="utf-8" />
 <meta name="viewport" content="width=device-width, initial-scale=1" />
 <title>Talteori översiktsföreläsning</title>
@@ -240,11 +240,11 @@ margin: 10px;
 <body>
 <header id="top" class="status">
 <div id="navbar" style ="text-align: center;">
-              <a href='https://liu.se'>LiU</a> -
-              <a href='https://liu.se/organisation/liu/mai'>MAI</a> -
-              <a href='https://liu.se/organisation/liu/mai'>Grundutbildning</a> -
-              <a href='https://courses.mai.liu.se/Lists/html/'>Kurser</a> -
-              <a href='index.html'>TATA54</a></div>
+                          <a href='https://liu.se'>LiU</a> -
+                          <a href='https://liu.se/organisation/liu/mai'>MAI</a> -
+                          <a href='https://liu.se/organisation/liu/mai'>Grundutbildning</a> -
+                          <a href='https://courses.mai.liu.se/Lists/html/'>Kurser</a> -
+                          <a href='index.html'>TATA54</a></div>
 </header>
 <main id="content" class="content">
 <header>
@@ -276,10 +276,10 @@ margin: 10px;
 <div class="outline-text-3" id="text-primtalsräkning">
 </div>
 
-<div id="outline-container-org2af6cb7" class="outline-4">
-<h4 id="org2af6cb7"><span class="section-number-4">1.1.1.</span> Primtalsräknarfunktionen</h4>
+<div id="outline-container-org45447a0" class="outline-4">
+<h4 id="org45447a0"><span class="section-number-4">1.1.1.</span> Primtalsräknarfunktionen</h4>
 <div class="outline-text-4" id="text-1-1-1">
-<div class="definition" id="org9039127">
+<div class="definition" id="orgeb70eab">
 <p>
 \(\pi(x) = \sum_{k \le x} \mathrm{IsPrime}(k)\)
 </p>
@@ -287,7 +287,7 @@ margin: 10px;
 </div>
 
 
-<div class="theorem" id="orgc80f0b9">
+<div class="theorem" id="org17daf5c">
 <p>
 \(\pi(x) \sim \frac{x}{\log x}\) då \(x \to \infty\).
 </p>
@@ -297,11 +297,11 @@ margin: 10px;
 </div>
 
 
-<div id="outline-container-orga3f0554" class="outline-4">
-<h4 id="orga3f0554"><span class="section-number-4">1.1.2.</span> Hadamard</h4>
+<div id="outline-container-orgd34e969" class="outline-4">
+<h4 id="orgd34e969"><span class="section-number-4">1.1.2.</span> Hadamard</h4>
 <div class="outline-text-4" id="text-1-1-2">
 
-<figure id="orgced749d">
+<figure id="orge3c1c3c">
 <img src="../img/wikiHadamard.jpg" alt="wikiHadamard.jpg">
 
 <figcaption><span class="figure-number">Illustration 1 </span>Hadamard</figcaption>
@@ -309,24 +309,24 @@ margin: 10px;
 </div>
 </div>
 
-<div id="outline-container-org8682363" class="outline-4">
-<h4 id="org8682363"><span class="section-number-4">1.1.3.</span> Primtalens täthet</h4>
+<div id="outline-container-org632b497" class="outline-4">
+<h4 id="org632b497"><span class="section-number-4">1.1.3.</span> Primtalens täthet</h4>
 <div class="outline-text-4" id="text-1-1-3">
-<div class="definition" id="org6a0f093">
+<div class="definition" id="org5ff0715">
 <p>
 Primtalstäthetsfunktion \(\pi(x)/x\).
 </p>
 
 </div>
 
-<div class="theorem" id="org466aa4e">
+<div class="theorem" id="org50be3a0">
 <p>
 \(\pi(x)/x \sim 1/\log(x)\).
 </p>
 
 </div>
 
-<div class="proof" id="orgf0bf128">
+<div class="proof" id="orgb72f116">
 <p>
 Följer av primtalssatsen.
 </p>
@@ -349,10 +349,10 @@ primtal \(\le 1000\).
 </div>
 </div>
 
-<div id="outline-container-orgad7f8ad" class="outline-4">
-<h4 id="orgad7f8ad"><span class="section-number-4">1.1.4.</span> Approximation av primtalstäthet</h4>
+<div id="outline-container-orge130570" class="outline-4">
+<h4 id="orge130570"><span class="section-number-4">1.1.4.</span> Approximation av primtalstäthet</h4>
 <div class="outline-text-4" id="text-1-1-4">
-<div class="theorem" id="orgff1fc81">
+<div class="theorem" id="org97f6cf0">
 <p>
 \(p(x)/x = \sum_{k=1}^{n-1} \frac{(k-1)!}{\log(x)^k} +
     \mathcal{O}\left( \frac{(n-1)!}{(log(x)^n)} \right)\) as
@@ -362,7 +362,7 @@ primtal \(\le 1000\).
 </div>
 
 
-<figure id="org9113ffd">
+<figure id="orga3fb710">
 <img src="prim-funk-approx.png" alt="prim-funk-approx.png">
 
 <figcaption><span class="figure-number">Illustration 2 </span>Första tre approximationerna till primtalstäthetsfunktionen</figcaption>
@@ -472,7 +472,7 @@ innehåller \(D\) gitterpunkt skild från origo.
 </p>
 
 
-<figure id="org810adab">
+<figure id="org25e12e6">
 <img src="wikikowski.png" alt="wikikowski.png">
 
 </figure>
@@ -701,7 +701,7 @@ komplicerad kombinatorik</li>
 <footer id="postamble" class="status">
 <p class="date">Datum: 2024-01-13</p>
 <p class="author">F&ouml;rfattare: Jan Snellman</p>
-<p class="date">Created: 2024-02-06</p>
+<p class="date">Created: 2024-08-22</p>
 <p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p>
 </footer>
 </body>
diff --git a/public/newlectures/newlecture.html b/public/newlectures/newlecture.html
index 6779d359563d4be83ab70eb91b311d81646375f5..a707d249d97131e4a16fe8512d8d55c4d9d132dd 100644
--- a/public/newlectures/newlecture.html
+++ b/public/newlectures/newlecture.html
@@ -1,7 +1,7 @@
 <!DOCTYPE html>
 <html lang="sv">
 <head>
-<!-- 2024-02-06 -->
+<!-- 2024-08-22 -->
 <meta charset="utf-8" />
 <meta name="viewport" content="width=device-width, initial-scale=1" />
 <title>Föreläsningar i Talteori</title>
@@ -230,11 +230,11 @@
 <body>
 <header id="top" class="status">
 <div id="navbar" style ="text-align: center;">
-              <a href='https://liu.se'>LiU</a> -
-              <a href='https://liu.se/organisation/liu/mai'>MAI</a> -
-              <a href='https://liu.se/organisation/liu/mai'>Grundutbildning</a> -
-              <a href='https://courses.mai.liu.se/Lists/html/'>Kurser</a> -
-              <a href='index.html'>TATA54</a></div>
+                          <a href='https://liu.se'>LiU</a> -
+                          <a href='https://liu.se/organisation/liu/mai'>MAI</a> -
+                          <a href='https://liu.se/organisation/liu/mai'>Grundutbildning</a> -
+                          <a href='https://courses.mai.liu.se/Lists/html/'>Kurser</a> -
+                          <a href='index.html'>TATA54</a></div>
 </header>
 <main id="content" class="content">
 <header>
@@ -243,8 +243,8 @@
 <h2>Inneh&aring;ll</h2>
 <div id="text-table-of-contents" role="doc-toc">
 <ul>
-<li><a href="#orgbf7615a">1. Introduktion</a></li>
-<li><a href="#org6fea25c">2. Kongruensräkning</a>
+<li><a href="#orgd9f10a0">1. Introduktion</a></li>
+<li><a href="#org328cad5">2. Kongruensräkning</a>
 <ul>
 <li><a href="#delbarhet">2.1. Delbarhet</a>
 <ul>
@@ -260,25 +260,25 @@
 </li>
 </ul>
 </li>
-<li><a href="#org6a9dc81">3. Aritmetiska funktioner</a></li>
-<li><a href="#orged85f3a">4. Hensel-lyft</a></li>
-<li><a href="#orga4ca7ab">5. Primitiva rötter</a></li>
-<li><a href="#orge5a8741">6. Kvadratiska residyer</a></li>
-<li><a href="#org2e926bc">7. Kvadratisk reciprocitet</a></li>
-<li><a href="#orgedcfbaa">8. Kedjebråk</a></li>
-<li><a href="#org557cc8f">9. Icke-linjära diofantiska ekvationer</a></li>
-<li><a href="#org1c08b0a">10. Gaussiska heltal</a></li>
-<li><a href="#orgdc134b1">11. Övrigt</a></li>
+<li><a href="#org6907ef0">3. Aritmetiska funktioner</a></li>
+<li><a href="#org91936fe">4. Hensel-lyft</a></li>
+<li><a href="#org60aa502">5. Primitiva rötter</a></li>
+<li><a href="#org43aac80">6. Kvadratiska residyer</a></li>
+<li><a href="#org14febe8">7. Kvadratisk reciprocitet</a></li>
+<li><a href="#org104725a">8. Kedjebråk</a></li>
+<li><a href="#org1e6ef78">9. Icke-linjära diofantiska ekvationer</a></li>
+<li><a href="#orgc9e8006">10. Gaussiska heltal</a></li>
+<li><a href="#orged8c772">11. Övrigt</a></li>
 </ul>
 </div>
 </nav>
 
-<section id="outline-container-orgbf7615a" class="outline-2">
-<h2 id="orgbf7615a"><span class="section-number-2">1.</span> Introduktion</h2>
+<section id="outline-container-orgd9f10a0" class="outline-2">
+<h2 id="orgd9f10a0"><span class="section-number-2">1.</span> Introduktion</h2>
 </section>
 
-<section id="outline-container-org6fea25c" class="outline-2">
-<h2 id="org6fea25c"><span class="section-number-2">2.</span> Kongruensräkning</h2>
+<section id="outline-container-org328cad5" class="outline-2">
+<h2 id="org328cad5"><span class="section-number-2">2.</span> Kongruensräkning</h2>
 <div class="outline-text-2" id="text-2">
 </div>
 <div id="outline-container-delbarhet" class="outline-3">
@@ -345,7 +345,7 @@ Om inte annat sägs så \(a,b,c,x,y,r,s \in {\mathbb{Z}}\), men
 <h4 id="partial-order"><span class="section-number-4">2.1.3.</span> Partial order</h4>
 <div class="outline-text-4" id="text-partial-order">
 
-<figure id="orge252b57">
+<figure id="org7c82efd">
 <img src="divisorlattice7.png" alt="divisorlattice7.png">
 
 <figcaption><span class="figure-number">Illustration 1 </span>Heltalen under delbarhet</figcaption>
@@ -833,7 +833,7 @@ Algorithm
 
 <div class="org-center">
 
-<figure id="orgbdb8fe6">
+<figure id="org806be6c">
 <img src="sieveE.jpg" alt="sieveE.jpg">
 
 </figure>
@@ -885,7 +885,7 @@ villkoret nödvändigt.
 </div>
 </li>
 
-<li><a id="org03cfdf4"></a>Dirichlet<br>
+<li><a id="orgd4329fe"></a>Dirichlet<br>
 <div class="outline-text-6" id="text-2-1-8-2-2">
 </div>
 </li>
@@ -896,38 +896,38 @@ villkoret nödvändigt.
 </div>
 </section>
 
-<section id="outline-container-org6a9dc81" class="outline-2">
-<h2 id="org6a9dc81"><span class="section-number-2">3.</span> Aritmetiska funktioner</h2>
+<section id="outline-container-org6907ef0" class="outline-2">
+<h2 id="org6907ef0"><span class="section-number-2">3.</span> Aritmetiska funktioner</h2>
 </section>
-<section id="outline-container-orged85f3a" class="outline-2">
-<h2 id="orged85f3a"><span class="section-number-2">4.</span> Hensel-lyft</h2>
+<section id="outline-container-org91936fe" class="outline-2">
+<h2 id="org91936fe"><span class="section-number-2">4.</span> Hensel-lyft</h2>
 </section>
-<section id="outline-container-orga4ca7ab" class="outline-2">
-<h2 id="orga4ca7ab"><span class="section-number-2">5.</span> Primitiva rötter</h2>
+<section id="outline-container-org60aa502" class="outline-2">
+<h2 id="org60aa502"><span class="section-number-2">5.</span> Primitiva rötter</h2>
 </section>
-<section id="outline-container-orge5a8741" class="outline-2">
-<h2 id="orge5a8741"><span class="section-number-2">6.</span> Kvadratiska residyer</h2>
+<section id="outline-container-org43aac80" class="outline-2">
+<h2 id="org43aac80"><span class="section-number-2">6.</span> Kvadratiska residyer</h2>
 </section>
-<section id="outline-container-org2e926bc" class="outline-2">
-<h2 id="org2e926bc"><span class="section-number-2">7.</span> Kvadratisk reciprocitet</h2>
+<section id="outline-container-org14febe8" class="outline-2">
+<h2 id="org14febe8"><span class="section-number-2">7.</span> Kvadratisk reciprocitet</h2>
 </section>
-<section id="outline-container-orgedcfbaa" class="outline-2">
-<h2 id="orgedcfbaa"><span class="section-number-2">8.</span> Kedjebråk</h2>
+<section id="outline-container-org104725a" class="outline-2">
+<h2 id="org104725a"><span class="section-number-2">8.</span> Kedjebråk</h2>
 </section>
-<section id="outline-container-org557cc8f" class="outline-2">
-<h2 id="org557cc8f"><span class="section-number-2">9.</span> Icke-linjära diofantiska ekvationer</h2>
+<section id="outline-container-org1e6ef78" class="outline-2">
+<h2 id="org1e6ef78"><span class="section-number-2">9.</span> Icke-linjära diofantiska ekvationer</h2>
 </section>
-<section id="outline-container-org1c08b0a" class="outline-2">
-<h2 id="org1c08b0a"><span class="section-number-2">10.</span> Gaussiska heltal</h2>
+<section id="outline-container-orgc9e8006" class="outline-2">
+<h2 id="orgc9e8006"><span class="section-number-2">10.</span> Gaussiska heltal</h2>
 </section>
-<section id="outline-container-orgdc134b1" class="outline-2">
-<h2 id="orgdc134b1"><span class="section-number-2">11.</span> Övrigt</h2>
+<section id="outline-container-orged8c772" class="outline-2">
+<h2 id="orged8c772"><span class="section-number-2">11.</span> Övrigt</h2>
 </section>
 </main>
 <footer id="postamble" class="status">
 <p class="date">Datum: 2024-01-13</p>
 <p class="author">F&ouml;rfattare: Jan Snellman</p>
-<p class="date">Created: 2024-02-06</p>
+<p class="date">Created: 2024-08-22</p>
 <p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p>
 </footer>
 </body>
diff --git a/public/senaste-nytt.html b/public/senaste-nytt.html
index 1ad694954ce236d8245a5862683ae45d07955889..c488eb5f729908ab10ff32645c05c41a2954a5f5 100644
--- a/public/senaste-nytt.html
+++ b/public/senaste-nytt.html
@@ -1,7 +1,7 @@
 <!DOCTYPE html>
 <html lang="en">
 <head>
-<!-- 2024-02-06 -->
+<!-- 2024-08-22 -->
 <meta charset="utf-8" />
 <meta name="viewport" content="width=device-width, initial-scale=1" />
 <title>&lrm;</title>
@@ -196,23 +196,23 @@
 <body>
 <header id="top" class="status">
 <div id="navbar" style ="text-align: center;">
-              <a href='https://liu.se'>LiU</a> -
-              <a href='https://liu.se/organisation/liu/mai'>MAI</a> -
-              <a href='https://liu.se/organisation/liu/mai'>Grundutbildning</a> -
-              <a href='https://courses.mai.liu.se/Lists/html/'>Kurser</a> -
-              <a href='index.html'>TATA54</a></div>
+                          <a href='https://liu.se'>LiU</a> -
+                          <a href='https://liu.se/organisation/liu/mai'>MAI</a> -
+                          <a href='https://liu.se/organisation/liu/mai'>Grundutbildning</a> -
+                          <a href='https://courses.mai.liu.se/Lists/html/'>Kurser</a> -
+                          <a href='index.html'>TATA54</a></div>
 </header>
 <main id="content" class="content">
 
 
 
-<section id="outline-container-org83ece8d" class="outline-2">
-<h2 id="org83ece8d">TATA54 Anteckningar från tidigare år</h2>
-<div class="outline-text-2" id="text-org83ece8d">
+<section id="outline-container-orgacdba95" class="outline-2">
+<h2 id="orgacdba95">TATA54 Anteckningar från tidigare år</h2>
+<div class="outline-text-2" id="text-orgacdba95">
 </div>
-<div id="outline-container-orgb8552ba" class="outline-3">
-<h3 id="orgb8552ba">2023</h3>
-<div class="outline-text-3" id="text-orgb8552ba">
+<div id="outline-container-orgd75a871" class="outline-3">
+<h3 id="orgd75a871">2023</h3>
+<div class="outline-text-3" id="text-orgd75a871">
 <ul class="org-ul">
 <li>2023-12-21: Gjorde klart <a href="index.html">denna nya kurshemsida</a>.</li>
 <li>2023-06-05: Jag har rättat tentan; en
@@ -266,9 +266,9 @@ tryckfel (skall vara w(d)). 7.2.38 är komplicerad och kan skippas.</li>
 </div>
 
 
-<div id="outline-container-orgc048d37" class="outline-3">
-<h3 id="orgc048d37">2021</h3>
-<div class="outline-text-3" id="text-orgc048d37">
+<div id="outline-container-orgf4540a0" class="outline-3">
+<h3 id="orgf4540a0">2021</h3>
+<div class="outline-text-3" id="text-orgf4540a0">
 <ul class="org-ul">
 <li>2021-20-26: Alla klarade omtentan, trots att uppgift 5 kanske var
 oklar, jag menade periodLÄNGD för decimalutvecklingen, den kan
@@ -316,9 +316,9 @@ någon inbjudan, så mejla mig.</li>
 </div>
 </div>
 
-<div id="outline-container-orgcebf283" class="outline-3">
-<h3 id="orgcebf283">2020</h3>
-<div class="outline-text-3" id="text-orgcebf283">
+<div id="outline-container-orgd33d225" class="outline-3">
+<h3 id="orgd33d225">2020</h3>
+<div class="outline-text-3" id="text-orgd33d225">
 <ul class="org-ul">
 <li><p>
 2020-12-12: Kursen kommer att ges VT2021, med start den 19e januari.
@@ -371,9 +371,9 @@ someone else (perhaps
 </div>
 </div>
 
-<div id="outline-container-orgc11f03a" class="outline-3">
-<h3 id="orgc11f03a">2019</h3>
-<div class="outline-text-3" id="text-orgc11f03a">
+<div id="outline-container-org01726fb" class="outline-3">
+<h3 id="org01726fb">2019</h3>
+<div class="outline-text-3" id="text-org01726fb">
 <ul class="org-ul">
 <li>2019-11-01: The course will not be given spring 2020.</li>
 
@@ -388,9 +388,9 @@ available.</li>
 </div>
 </div>
 
-<div id="outline-container-org39bfc1f" class="outline-3">
-<h3 id="org39bfc1f">2018</h3>
-<div class="outline-text-3" id="text-org39bfc1f">
+<div id="outline-container-org2020805" class="outline-3">
+<h3 id="org2020805">2018</h3>
+<div class="outline-text-3" id="text-org2020805">
 <ul class="org-ul">
 <li>2018-06-08: <a href="exams/2018/tentaTATA5420180607soln.pdf">Solutions</a> to
 <a href="exams/2018/tenta20180607.pdf">the exam on June 7</a> are now
@@ -403,9 +403,9 @@ available.</li>
 </div>
 </div>
 
-<div id="outline-container-org3f27bad" class="outline-3">
-<h3 id="org3f27bad">2017</h3>
-<div class="outline-text-3" id="text-org3f27bad">
+<div id="outline-container-orga47b531" class="outline-3">
+<h3 id="orga47b531">2017</h3>
+<div class="outline-text-3" id="text-orga47b531">
 <ul class="org-ul">
 <li>2017-08-28: <a href="exams/2017/tentaTATA54170826soln.pdf">Solutions</a> to
 <a href="exams/2017/tenta170826.pdf">the exam on Saturday 26</a> are now
@@ -428,7 +428,7 @@ Another text is <a href="https://wstein.org/ent/">Elementary Number Theory</a> a
 </ul>
 
 
-<figure id="org4f39495">
+<figure id="org643f358">
 <img src="img/sieveE.jpg" alt="sieveE.jpg">
 
 </figure>
@@ -438,7 +438,7 @@ Another text is <a href="https://wstein.org/ent/">Elementary Number Theory</a> a
 </main>
 <footer id="postamble" class="status">
 <p class="author">Author: Jan Snellman</p>
-<p class="date">Created: 2024-02-06</p>
+<p class="date">Created: 2024-08-22</p>
 <p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p>
 </footer>
 </body>
diff --git a/public/sitemap.html b/public/sitemap.html
index d3b306c3849d95927b6ce9a106c73dec29ddfc20..64e5f08f906c91dba039c6075c55ff819e0b35e8 100644
--- a/public/sitemap.html
+++ b/public/sitemap.html
@@ -1,7 +1,7 @@
 <!DOCTYPE html>
 <html lang="en">
 <head>
-<!-- 2024-06-05 -->
+<!-- 2024-08-22 -->
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 <title>Kurshemsida</title>
@@ -206,24 +206,24 @@
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 <h1 class="title">Kurshemsida</h1>
 </header><ul class="org-ul">
-<li><a href="newlectures/newlecture.html">Föreläsningar i Talteori</a></li>
-<li><a href="newlectures/new-lect-0.html">Talteori översiktsföreläsning</a></li>
+<li><a href="index.html">TATA54 Talteori</a></li>
+<li><a href="senaste-nytt.html">senaste-nytt</a></li>
+<li><a href="lectures/Henselfaktorisering.html">Henselfaktorisering</a></li>
 <li><a href="labs/lecture5.html">lecture5</a></li>
 <li><a href="labs/lecture4.html">lecture4</a></li>
 <li><a href="labs/lecture3.html">lecture3</a></li>
 <li><a href="labs/lecture2.html">lecture2</a></li>
 <li><a href="labs/lecture1.html">lecture1</a></li>
 <li><a href="labs/lecture0.html">lecture0</a></li>
-<li><a href="index.html">TATA54 Talteori</a></li>
-<li><a href="senaste-nytt.html">senaste-nytt</a></li>
 <li><a href="labs/kedjebraklab.html">Sagemath-övningar på kedjebråk</a></li>
 <li><a href="labs/HenselLyftLabHT2023.html">SageMath-övningar på Hensellyft, primitiva rötter, och KRS</a></li>
-<li><a href="lectures/Henselfaktorisering.html">Henselfaktorisering</a></li>
+<li><a href="newlectures/newlecture.html">Föreläsningar i Talteori</a></li>
+<li><a href="newlectures/new-lect-0.html">Talteori översiktsföreläsning</a></li>
 </ul>
 </main>
 <footer id="postamble" class="status">
 <p class="author">Author: Jan Snellman</p>
-<p class="date">Created: 2024-06-05</p>
+<p class="date">Created: 2024-08-22</p>
 <p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p>
 </footer>
 </body>