From 0ef8552369e85a172dcd8efe741e815646b2e528 Mon Sep 17 00:00:00 2001
From: Jan Snellman <jan.snellman@liu.se>
Date: Fri, 23 Aug 2024 12:58:31 +0200
Subject: [PATCH] =?UTF-8?q?fixade=20l=C3=B6sning=2020240822?=
MIME-Version: 1.0
Content-Type: text/plain; charset=UTF-8
Content-Transfer-Encoding: 8bit

---
 .../TENTOR/#tenta-TATA54-20240822-skiss.org#  |  62 +-
 .../TENTOR/.#tenta-TATA54-20240822-skiss.org  |   2 +-
 .../TENTOR/tenta-TATA54-20240822-losning.log  |  53 +-
 .../TENTOR/tenta-TATA54-20240822-losning.pdf  | Bin 110723 -> 110101 bytes
 .../TENTOR/tenta-TATA54-20240822-losning.tex  |   7 +-
 TATA54/TENTOR/tenta-TATA54-20240822-skiss.org |   2 +-
 .../2024/tenta-TATA54-20240822-losning.pdf    | Bin 110723 -> 110101 bytes
 homepage/sitemap.org                          |   8 +-
 .../2024/tenta-TATA54-20240822-losning.pdf    | Bin 110723 -> 110101 bytes
 public/index.html                             | 686 +++++++++---------
 public/sitemap.html                           |  10 +-
 11 files changed, 408 insertions(+), 422 deletions(-)

diff --git a/TATA54/TENTOR/#tenta-TATA54-20240822-skiss.org# b/TATA54/TENTOR/#tenta-TATA54-20240822-skiss.org#
index fb6577b..78b46aa 100644
--- a/TATA54/TENTOR/#tenta-TATA54-20240822-skiss.org#
+++ b/TATA54/TENTOR/#tenta-TATA54-20240822-skiss.org#
@@ -41,20 +41,19 @@ def H_L_tree(f, p: int, r: int):
 #+end_src
 
 
-#+begin_src sage
-  :session 
-   p = 5
-   k = 4
-   q = p^k
-   R.<x> = ZZ[]
-   f = x^4 + 2*x + 3
-   [(s,f.roots(Integers(p^s),multiplicities=False)) for s in range(k+1)]
-   df = f.diff()
-   df, df(3)
+#+begin_src sage :session 
+  p = 5
+  k = 4
+  q = p^k
+  R.<x> = ZZ[]
+  f = x^4 + 2*x + 4
+  [(s,f.roots(Integers(p^s),multiplicities=False)) for s in range(k+1)]
+  df = f.diff()
+  df, df(3)
 #+end_src
 
 #+RESULTS:
-: [(0, [0]), (1, [3]), (2, []), (3, []), (4, [])]
+: [(0, [0]), (1, []), (2, []), (3, []), (4, [])]
 : (4*x^3 + 2, 110)
 
 #+begin_src sage :session :results file :file "nu1.png"
@@ -78,17 +77,16 @@ def H_L_tree(f, p: int, r: int):
 
 Parametrisera med lutning, rationell punkt (-1,0)
 
-#+begin_src sage
-  :session
-  var('s,t,x,y')
-  kurva = x^2 + 2*y^2-1
-  linje = y - t*(x+1)
-  soln = solve([kurva,linje],[x,y])
-  soln
-  rp = soln[0]
-  rp
-  soln2 = solve([linje],[t])
-  soln2
+#+begin_src sage :session
+var('s,t,x,y')
+kurva = x^2 + 2*y^2-1
+linje = y - t*(x+1)
+soln = solve([kurva,linje],[x,y])
+soln
+rp = soln[0]
+rp
+soln2 = solve([linje],[t])
+soln2
 #+end_src
 
 #+RESULTS:
@@ -106,12 +104,7 @@ parametric_plot((rp[0].rhs(),rp[1].rhs()), (t,+epsi,1/sqrt(7) -epsi) )
 [[file:nu2.png]]
 
 ** U3
-#+begin_src sage :session
-  legendre_symbol(187,23)
-#+end_src
 
-#+RESULTS:
-: 1
 
 ** U4 
 #+begin_src latex
@@ -122,8 +115,7 @@ parametric_plot((rp[0].rhs(),rp[1].rhs()), (t,+epsi,1/sqrt(7) -epsi) )
     \]
 #+end_src
 
-#+begin_s
-rc sage :session
+#+begin_src sage :session
 n=20
 [(k,number_of_divisors(k),floor(n/k)) for k in range(1,n+1)]
 
@@ -138,7 +130,6 @@ def w(n):
 #+end_src
 
 #+RESULTS:
-
 #+begin_example
 [(1, 1, 20),
  (2, 2, 10),
@@ -183,8 +174,6 @@ def w(n):
 #+end_example
 
 ** U5
-
-
 #+begin_src latex
 
 #+end_src
@@ -198,8 +187,7 @@ Hur många har
 #+end_export
 
 
-#+begin_src s
-age :session
+#+begin_src sage :session
 p = 23
 a = 11*17
 a
@@ -210,6 +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:
@@ -218,6 +209,7 @@ f.roots(Integers(17),multiplicities=False)
 : []
 : [10, 1]
 : []
+: [16, 7]
 
 ** U7
 #+begin_src latex
@@ -240,6 +232,7 @@ r=p/q
 cf = continued_fraction(r)
 cf
 best = cf.convergent(2)
+best
 fel = abs(p/q - best)
 "kedjebråkapprox fel", fel
 
@@ -254,6 +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/TATA54/TENTOR/.#tenta-TATA54-20240822-skiss.org b/TATA54/TENTOR/.#tenta-TATA54-20240822-skiss.org
index 98366ae..bf5a20e 120000
--- a/TATA54/TENTOR/.#tenta-TATA54-20240822-skiss.org
+++ b/TATA54/TENTOR/.#tenta-TATA54-20240822-skiss.org
@@ -1 +1 @@
-jansn@jansn19-thinkpad.130192:1724236765
\ No newline at end of file
+jansn@jansn19-thinkpad.315947:1724236765
\ No newline at end of file
diff --git a/TATA54/TENTOR/tenta-TATA54-20240822-losning.log b/TATA54/TENTOR/tenta-TATA54-20240822-losning.log
index e9be7f5..79a399c 100644
--- a/TATA54/TENTOR/tenta-TATA54-20240822-losning.log
+++ b/TATA54/TENTOR/tenta-TATA54-20240822-losning.log
@@ -1,9 +1,12 @@
-This is pdfTeX, Version 3.141592653-2.6-1.40.25 (TeX Live 2023/Fedora 40) (preloaded format=pdflatex 2024.8.22)  22 AUG 2024 20:38
+This is pdfTeX, Version 3.141592653-2.6-1.40.25 (TeX Live 2023/Fedora 40) (preloaded format=pdflatex 2024.8.21)  23 AUG 2024 12:53
 entering extended mode
  restricted \write18 enabled.
+ file:line:error style messages enabled.
  %&-line parsing enabled.
-**\nonstopmode\input tenta-TATA54-20240822-losning.tex
+**tenta-TATA54-20240822-losning.tex
 (./tenta-TATA54-20240822-losning.tex
+LaTeX2e <2022-11-01> patch level 1
+L3 programming layer <2023-02-22>
 (/usr/share/texlive/texmf-dist/tex/latex/base/article.cls
 Document Class: article 2022/07/02 v1.4n Standard LaTeX document class
 (/usr/share/texlive/texmf-dist/tex/latex/base/size10.clo
@@ -131,7 +134,7 @@ Package: inputenc 2021/02/14 v1.3d Input encoding file
 Package: babel 2023/02/13 3.86 The Babel package
 \babel@savecnt=\count271
 \U@D=\dimen150
-\l@unhyphenated=\language3
+\l@unhyphenated=\language85
 
 (/usr/share/texlive/texmf-dist/tex/generic/babel/txtbabel.def)
 \bbl@readstream=\read2
@@ -139,21 +142,13 @@ Package: babel 2023/02/13 3.86 The Babel package
 
 (/usr/share/texlive/texmf-dist/tex/generic/babel-swedish/swedish.ldf
 Language: swedish 2021/02/06 v2.3e Swedish support from the babel system
-
-
-Package babel Warning: No hyphenation patterns were preloaded for
-(babel)                the language 'Swedish' into the format.
-(babel)                Please, configure your TeX system to add them and
-(babel)                rebuild the format. Now I will use the patterns
-(babel)                preloaded for \language=0 instead on input line 49.
-
-Package babel Info: Hyphen rules for 'swedish' set to \l@english
-(babel)             (\language0). Reported on input line 50.
 Package babel Info: Making " an active character on input line 90.
-)) (/usr/share/texlive/texmf-dist/tex/generic/babel/locale/sv/babel-swedish.tex
+))
+(/usr/share/texlive/texmf-dist/tex/generic/babel/locale/sv/babel-swedish.tex
 Package babel Info: Importing font and identification data for swedish
 (babel)             from babel-sv.ini. Reported on input line 11.
-) (/usr/share/texlive/texmf-dist/tex/latex/l3backend/l3backend-pdftex.def
+)
+(/usr/share/texlive/texmf-dist/tex/latex/l3backend/l3backend-pdftex.def
 File: l3backend-pdftex.def 2023-01-16 L3 backend support: PDF output (pdfTeX)
 \l__color_backend_stack_int=\count273
 \l__pdf_internal_box=\box53
@@ -187,13 +182,13 @@ LaTeX Font Info:    Trying to load font information for U+msb on input line 35.
 (/usr/share/texlive/texmf-dist/tex/latex/amsfonts/umsb.fd
 File: umsb.fd 2013/01/14 v3.01 AMS symbols B
 )
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-[]\OT1/cmr/bx/n/10 L[]osning: \OT1/cmr/m/n/10 Ked-je-br^^Waksutvecklingen []ar 
-$117\OML/cmm/m/it/10 =\OT1/cmr/m/n/10 118 = [0; 1\OML/cmm/m/it/10 ; \OT1/cmr/m/
-n/10 58\OML/cmm/m/it/10 ; \OT1/cmr/m/n/10 2]$ med kon-ver-gen-ter $0\OML/cmm/m/
-it/10 ; \OT1/cmr/m/n/10 1\OML/cmm/m/it/10 ; \OT1/cmr/m/n/10 58\OML/cmm/m/it/10 
-=\OT1/cmr/m/n/10 59\OML/cmm/m/it/10 ; \OT1/cmr/m/n/10 117\OML/cmm/m/it/10 =\OT1
-/cmr/m/n/10 118$.
+Overfull \hbox (9.70393pt too wide) in paragraph at lines 86--91
+[]\OT1/cmr/bx/n/10 L[]osning: \OT1/cmr/m/n/10 Ked-jebr^^Waksutvecklingen []ar $
+117\OML/cmm/m/it/10 =\OT1/cmr/m/n/10 118 = [0; 1\OML/cmm/m/it/10 ; \OT1/cmr/m/n
+/10 58\OML/cmm/m/it/10 ; \OT1/cmr/m/n/10 2]$ med kon-ver-gen-ter $0\OML/cmm/m/i
+t/10 ; \OT1/cmr/m/n/10 1\OML/cmm/m/it/10 ; \OT1/cmr/m/n/10 58\OML/cmm/m/it/10 =
+\OT1/cmr/m/n/10 59\OML/cmm/m/it/10 ; \OT1/cmr/m/n/10 117\OML/cmm/m/it/10 =\OT1/
+cmr/m/n/10 118$.
  []
 
 [1
@@ -201,13 +196,13 @@ it/10 ; \OT1/cmr/m/n/10 1\OML/cmm/m/it/10 ; \OT1/cmr/m/n/10 58\OML/cmm/m/it/10
 {/var/lib/texmf/fonts/map/pdftex/updmap/pdftex.map}]
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- 46908 string characters out of 5842640
- 1864388 words of memory out of 6000000
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+ 2935 strings out of 476041
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+ 1863388 words of memory out of 6000000
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  514294 words of font info for 41 fonts, out of 8000000 for 9000
- 14 hyphenation exceptions out of 8191
- 56i,9n,62p,271b,219s stack positions out of 10000i,1000n,20000p,200000b,200000s
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-Output written on tenta-TATA54-20240822-losning.pdf (1 page, 110723 bytes).
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diff --git a/TATA54/TENTOR/tenta-TATA54-20240822-losning.tex b/TATA54/TENTOR/tenta-TATA54-20240822-losning.tex
index 0c1a8b6..3203841 100644
--- a/TATA54/TENTOR/tenta-TATA54-20240822-losning.tex
+++ b/TATA54/TENTOR/tenta-TATA54-20240822-losning.tex
@@ -36,11 +36,8 @@ Examinator: Jan Snellman}
     x^4 +2x +4 \equiv 0 \mod 625 ?
   \end{displaymath}
 
-  \soln Kalla polynomet för \(f(x)\). Modulo 5 finns den enda lösningen
-  \(x \equiv 3 \mod 5\). Eftersom \(f'(3)=110 \equiv 0 \mod 5\)
-  så lyfter inga eller alla av \(3 + 5s\), \(s=0,1,2,3,4\),
-  till lösningar modulo 25. Eftersom \(f(3)=110 \not \equiv 0\)
-  så finns inga lösningar modulo 25, och alltså inga modulo 625.
+  \soln Kalla polynomet för \(f(x)\). Modulo 5 finns
+  inga lösningar; alltså finns inga lösningar modulo \(5^4\).
 
 \item   Hitta alla rationella punkter på kurvan
    \begin{displaymath}
diff --git a/TATA54/TENTOR/tenta-TATA54-20240822-skiss.org b/TATA54/TENTOR/tenta-TATA54-20240822-skiss.org
index 922d776..5916c78 100644
--- a/TATA54/TENTOR/tenta-TATA54-20240822-skiss.org
+++ b/TATA54/TENTOR/tenta-TATA54-20240822-skiss.org
@@ -46,7 +46,7 @@ def H_L_tree(f, p: int, r: int):
   k = 4
   q = p^k
   R.<x> = ZZ[]
-  f = x^4 + 2*x + 3
+  f = x^4 + 2*x + 4
   [(s,f.roots(Integers(p^s),multiplicities=False)) for s in range(k+1)]
   df = f.diff()
   df, df(3)
diff --git a/homepage/exams/2024/tenta-TATA54-20240822-losning.pdf b/homepage/exams/2024/tenta-TATA54-20240822-losning.pdf
index 34f831aaf168f2a7b0660a02384565b351b6565c..02084b171957c977b9f32bab844b790b7a4fa52c 100644
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diff --git a/homepage/sitemap.org b/homepage/sitemap.org
index 89f0173..c1e5cb8 100644
--- a/homepage/sitemap.org
+++ b/homepage/sitemap.org
@@ -1,8 +1,10 @@
 #+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:senaste-nytt.org][senaste-nytt]]
 - [[file:labs/lecture5.org][lecture5]]
 - [[file:labs/lecture4.org][lecture4]]
 - [[file:labs/lecture3.org][lecture3]]
@@ -10,6 +12,4 @@
 - [[file:labs/lecture1.org][lecture1]]
 - [[file:labs/lecture0.org][lecture0]]
 - [[file:labs/kedjebraklab.org][Sagemath-övningar på kedjebråk]]
-- [[file:labs/HenselLyftLabHT2023.org][SageMath-övningar på Hensellyft, primitiva rötter, och KRS]]
-- [[file:newlectures/newlecture.org][Föreläsningar i Talteori]]
-- [[file:newlectures/new-lect-0.org][Talteori översiktsföreläsning]]
\ No newline at end of file
+- [[file:labs/HenselLyftLabHT2023.org][SageMath-övningar på Hensellyft, primitiva rötter, och KRS]]
\ 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
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diff --git a/public/index.html b/public/index.html
index cdfbbec..aabbb11 100644
--- a/public/index.html
+++ b/public/index.html
@@ -1,7 +1,7 @@
 <!DOCTYPE html>
 <html lang="sv">
 <head>
-<!-- 2024-08-22 -->
+<!-- 2024-08-23 -->
 <meta charset="utf-8" />
 <meta name="viewport" content="width=device-width, initial-scale=1" />
 <title>TATA54 Talteori</title>
@@ -63,151 +63,151 @@
 <h2>Inneh&aring;ll</h2>
 <div id="text-table-of-contents" role="doc-toc">
 <ul>
-<li><a href="#orgb8be38a">Kurshemsida för TATA54, Talteori  </a>
+<li><a href="#org8cf611f">Kurshemsida för TATA54, Talteori  </a>
 <ul>
-<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>
+<li><a href="#orgd386ff5">Ämnesområde</a></li>
+<li><a href="#org5fa7c84">Poäng</a></li>
+<li><a href="#org1941399">Examinator</a></li>
+<li><a href="#orgd6f97a6">Schema</a></li>
+<li><a href="#orgcbec67a">Examination</a></li>
 </ul>
 </li>
-<li><a href="#orge4d1d7b">Allra senaste nytt VT2024 </a>
+<li><a href="#orgda7b5cb">Allra senaste nytt VT2024 </a>
 <ul>
-<li><a href="#org79df182">2024-08-22</a></li>
-<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>
+<li><a href="#org3caa1c9">2024-08-22</a></li>
+<li><a href="#org5787ffb">2024-06-05</a></li>
+<li><a href="#org820103f">2024-06-01</a></li>
+<li><a href="#orgb795cef">2024-05-18</a></li>
+<li><a href="#orgef16020">2024-05-16</a></li>
+<li><a href="#orgd3edf39">2024-05-13</a></li>
+<li><a href="#orgbb2c19c">2024-05-06</a></li>
+<li><a href="#org6916c72">2024-04-29</a></li>
+<li><a href="#org2fc933f">2024-04-23</a></li>
+<li><a href="#org0e96bfa">2024-04-22</a></li>
+<li><a href="#org796ce06">2024-04-14</a>
 <ul>
-<li><a href="#orgfb7845d">Uppgifter att räkna till nästa gång</a></li>
-<li><a href="#orgef7eb4d">Datorlaboration</a></li>
+<li><a href="#org1198084">Uppgifter att räkna till nästa gång</a></li>
+<li><a href="#org87e8642">Datorlaboration</a></li>
 </ul>
 </li>
-<li><a href="#org4a80012">2024-04-07</a>
+<li><a href="#orgff00c35">2024-04-07</a>
 <ul>
-<li><a href="#org3f1c3a4">Uppgifter att räkna till nästa gång</a></li>
-<li><a href="#orgd77ff3b">Beviset för kvadratisk reciprocitet</a></li>
+<li><a href="#org10c6215">Uppgifter att räkna till nästa gång</a></li>
+<li><a href="#orgcb6d72a">Beviset för kvadratisk reciprocitet</a></li>
 </ul>
 </li>
-<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>
+<li><a href="#org84ac4df">2024-04-02</a></li>
+<li><a href="#orgecb5391">2024-03-11</a></li>
+<li><a href="#orged53d50">2024-03-06</a></li>
+<li><a href="#org69c699e">2024-03-05</a></li>
+<li><a href="#org8b45b59">2024-02-29</a></li>
+<li><a href="#org6ee578d">2024-02-20</a></li>
+<li><a href="#org15914f2">2024-02-12</a></li>
+<li><a href="#org445fa32">2024-02-07</a></li>
+<li><a href="#org887cf9c">2024-01-30</a>
 <ul>
-<li><a href="#org53dcc9b">Tvillingfria primtal</a></li>
+<li><a href="#orge760dad">Tvillingfria primtal</a></li>
 </ul>
 </li>
-<li><a href="#orgd22b4e6">2024-01-23</a></li>
-<li><a href="#org5900f63">2024-01-16</a></li>
+<li><a href="#org488e68b">2024-01-23</a></li>
+<li><a href="#org96d1546">2024-01-16</a></li>
 </ul>
 </li>
-<li><a href="#org4f543bd">Kurslitteratur </a>
+<li><a href="#org7fb0ecc">Kurslitteratur </a>
 <ul>
-<li><a href="#org09cac9a">Kursbok</a></li>
-<li><a href="#orgdf2c024">Bredvidläsning</a>
+<li><a href="#org1046eac">Kursbok</a></li>
+<li><a href="#orgb1f71c0">Bredvidläsning</a>
 <ul>
-<li><a href="#org9934079">Fritt tillgängligt material</a></li>
-<li><a href="#org486a906">Andra lämpliga böcker</a></li>
+<li><a href="#org1304ec9">Fritt tillgängligt material</a></li>
+<li><a href="#org156f528">Andra lämpliga böcker</a></li>
 </ul>
 </li>
 </ul>
 </li>
-<li><a href="#org83d546e">Kursinnehåll </a>
+<li><a href="#org777e787">Kursinnehåll </a>
 <ul>
-<li><a href="#org34795a7">Avsnitt av kursboken</a>
+<li><a href="#org8bd2546">Avsnitt av kursboken</a>
 <ul>
-<li><a href="#org10138de">Rekommenderade uppgifter </a></li>
+<li><a href="#org5c92b21">Rekommenderade uppgifter </a></li>
 </ul>
 </li>
-<li><a href="#orgab0c2e2">Kort beskrivning av kursinnehållet</a></li>
+<li><a href="#orgf97dd5f">Kort beskrivning av kursinnehållet</a></li>
 </ul>
 </li>
-<li><a href="#org67ef94b">Föreläsningar </a></li>
-<li><a href="#org9e66246">Tentor </a></li>
-<li><a href="#orgf236219">Datorlaborationer </a>
+<li><a href="#orgb1afa66">Föreläsningar </a></li>
+<li><a href="#orgd9a1a3d">Tentor </a></li>
+<li><a href="#orgaa8bfe8">Datorlaborationer </a>
 <ul>
-<li><a href="#org7a98c02">SageMath</a></li>
-<li><a href="#org38724a4">Kod från vissa föreläsningar</a></li>
-<li><a href="#org80ba8f8">Laborationer</a>
+<li><a href="#org0e9470f">SageMath</a></li>
+<li><a href="#org4e01f4d">Kod från vissa föreläsningar</a></li>
+<li><a href="#org771ae33">Laborationer</a>
 <ul>
-<li><a href="#org4bb0ea2">Hensellyft, Primitiva rötter, Kinesiska restsatsen</a></li>
-<li><a href="#org4f8b714">Kedjebråk</a></li>
+<li><a href="#orge16b88e">Hensellyft, Primitiva rötter, Kinesiska restsatsen</a></li>
+<li><a href="#org254ad94">Kedjebråk</a></li>
 </ul>
 </li>
 </ul>
 </li>
-<li><a href="#org65b020a">Tidigare år </a>
+<li><a href="#orgcab2c84">Tidigare år </a>
 <ul>
-<li><a href="#org477262d">TATA54 Anteckningar från tidigare år</a>
+<li><a href="#org5db15ec">TATA54 Anteckningar från tidigare år</a>
 <ul>
-<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>
+<li><a href="#org2e74361">2023</a></li>
+<li><a href="#org39f254e">2021</a></li>
+<li><a href="#orgab915cd">2020</a></li>
+<li><a href="#org51934a3">2019</a></li>
+<li><a href="#org51909e4">2018</a></li>
+<li><a href="#org50057cb">2017</a></li>
 </ul>
 </li>
 </ul>
 </li>
-<li><a href="#org22888c0">Index</a></li>
+<li><a href="#org27e935f">Index</a></li>
 </ul>
 </div>
 </nav>
 
-<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">
+<section id="outline-container-org8cf611f" class="outline-2">
+<h2 id="org8cf611f">Kurshemsida för TATA54, Talteori  <a id="org744b74f"></a></h2>
+<div class="outline-text-2" id="text-org8cf611f">
 </div>
-<div id="outline-container-org46c8838" class="outline-3">
-<h3 id="org46c8838">Ämnesområde</h3>
-<div class="outline-text-3" id="text-org46c8838">
+<div id="outline-container-orgd386ff5" class="outline-3">
+<h3 id="orgd386ff5">Ämnesområde</h3>
+<div class="outline-text-3" id="text-orgd386ff5">
 <p>
 Matematik
 </p>
 </div>
 </div>
-<div id="outline-container-org0536e03" class="outline-3">
-<h3 id="org0536e03">Poäng</h3>
-<div class="outline-text-3" id="text-org0536e03">
+<div id="outline-container-org5fa7c84" class="outline-3">
+<h3 id="org5fa7c84">Poäng</h3>
+<div class="outline-text-3" id="text-org5fa7c84">
 <p>
 6 hp
 </p>
 </div>
 </div>
-<div id="outline-container-org483cd31" class="outline-3">
-<h3 id="org483cd31">Examinator</h3>
-<div class="outline-text-3" id="text-org483cd31">
+<div id="outline-container-org1941399" class="outline-3">
+<h3 id="org1941399">Examinator</h3>
+<div class="outline-text-3" id="text-org1941399">
 <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-org79caf1d" class="outline-3">
-<h3 id="org79caf1d">Schema</h3>
-<div class="outline-text-3" id="text-org79caf1d">
+<div id="outline-container-orgd6f97a6" class="outline-3">
+<h3 id="orgd6f97a6">Schema</h3>
+<div class="outline-text-3" id="text-orgd6f97a6">
 <p>
 Se <a href="https://cloud.timeedit.net/liu/web/schema/ri167XQQ538Z50Qm07065gZ6y2Y7306Q6Y43Y1.html">TimeEdit</a>
 </p>
 </div>
 </div>
 
-<div id="outline-container-org3280174" class="outline-3">
-<h3 id="org3280174">Examination</h3>
-<div class="outline-text-3" id="text-org3280174">
+<div id="outline-container-orgcbec67a" class="outline-3">
+<h3 id="orgcbec67a">Examination</h3>
+<div class="outline-text-3" id="text-orgcbec67a">
 <p>
 Skriftlig tentamen.
 </p>
@@ -260,21 +260,21 @@ Skriftlig tentamen.
 </div>
 </div>
 </section>
-<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">
+<section id="outline-container-orgda7b5cb" class="outline-2">
+<h2 id="orgda7b5cb">Allra senaste nytt VT2024 <a id="org53d52c1"></a></h2>
+<div class="outline-text-2" id="text-orgda7b5cb">
 </div>
-<div id="outline-container-org79df182" class="outline-3">
-<h3 id="org79df182">2024-08-22</h3>
-<div class="outline-text-3" id="text-org79df182">
+<div id="outline-container-org3caa1c9" class="outline-3">
+<h3 id="org3caa1c9">2024-08-22</h3>
+<div class="outline-text-3" id="text-org3caa1c9">
 <p>
 <a href="exams/2024/tenta-TATA54-20240822-losning.pdf">Lösningar</a> till <a href="exams/2024/tenta-TATA54-20240822.pdf">dagens tenta</a> finns nu att beskåda.
 </p>
 </div>
 </div>
-<div id="outline-container-org4de2404" class="outline-3">
-<h3 id="org4de2404">2024-06-05</h3>
-<div class="outline-text-3" id="text-org4de2404">
+<div id="outline-container-org5787ffb" class="outline-3">
+<h3 id="org5787ffb">2024-06-05</h3>
+<div class="outline-text-3" id="text-org5787ffb">
 <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.
@@ -282,18 +282,18 @@ nästa vecka.
 </p>
 </div>
 </div>
-<div id="outline-container-org7866ed4" class="outline-3">
-<h3 id="org7866ed4">2024-06-01</h3>
-<div class="outline-text-3" id="text-org7866ed4">
+<div id="outline-container-org820103f" class="outline-3">
+<h3 id="org820103f">2024-06-01</h3>
+<div class="outline-text-3" id="text-org820103f">
 <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-org896f14e" class="outline-3">
-<h3 id="org896f14e">2024-05-18</h3>
-<div class="outline-text-3" id="text-org896f14e">
+<div id="outline-container-orgb795cef" class="outline-3">
+<h3 id="orgb795cef">2024-05-18</h3>
+<div class="outline-text-3" id="text-orgb795cef">
 <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>
@@ -304,13 +304,13 @@ 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="#orge3aa510">längre ned på denna sida</a>.
+Rosen, finns <a href="#orgd3a32bb">längre ned på denna sida</a>.
 </p>
 </div>
 </div>
-<div id="outline-container-org016a4e1" class="outline-3">
-<h3 id="org016a4e1">2024-05-16</h3>
-<div class="outline-text-3" id="text-org016a4e1">
+<div id="outline-container-orgef16020" class="outline-3">
+<h3 id="orgef16020">2024-05-16</h3>
+<div class="outline-text-3" id="text-orgef16020">
 <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.
@@ -321,35 +321,35 @@ Tentamen skall kunna bli av utan problem!
 </p>
 </div>
 </div>
-<div id="outline-container-org4232b8e" class="outline-3">
-<h3 id="org4232b8e">2024-05-13</h3>
-<div class="outline-text-3" id="text-org4232b8e">
+<div id="outline-container-orgd3edf39" class="outline-3">
+<h3 id="orgd3edf39">2024-05-13</h3>
+<div class="outline-text-3" id="text-orgd3edf39">
 <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-org95a2714" class="outline-3">
-<h3 id="org95a2714">2024-05-06</h3>
-<div class="outline-text-3" id="text-org95a2714">
+<div id="outline-container-orgbb2c19c" class="outline-3">
+<h3 id="orgbb2c19c">2024-05-06</h3>
+<div class="outline-text-3" id="text-orgbb2c19c">
 <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-orgcae408e" class="outline-3">
-<h3 id="orgcae408e">2024-04-29</h3>
-<div class="outline-text-3" id="text-orgcae408e">
+<div id="outline-container-org6916c72" class="outline-3">
+<h3 id="org6916c72">2024-04-29</h3>
+<div class="outline-text-3" id="text-org6916c72">
 <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-org9f9d6f3" class="outline-3">
-<h3 id="org9f9d6f3">2024-04-23</h3>
-<div class="outline-text-3" id="text-org9f9d6f3">
+<div id="outline-container-org2fc933f" class="outline-3">
+<h3 id="org2fc933f">2024-04-23</h3>
+<div class="outline-text-3" id="text-org2fc933f">
 <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
@@ -362,9 +362,9 @@ beskrivningen kan visas med induktion.
 </p>
 </div>
 </div>
-<div id="outline-container-orgb23df4f" class="outline-3">
-<h3 id="orgb23df4f">2024-04-22</h3>
-<div class="outline-text-3" id="text-orgb23df4f">
+<div id="outline-container-org0e96bfa" class="outline-3">
+<h3 id="org0e96bfa">2024-04-22</h3>
+<div class="outline-text-3" id="text-org0e96bfa">
 <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).
@@ -372,21 +372,21 @@ Till på fredag 12.4.5b, 12.4.6b
 </p>
 </div>
 </div>
-<div id="outline-container-org6bf16cd" class="outline-3">
-<h3 id="org6bf16cd">2024-04-14</h3>
-<div class="outline-text-3" id="text-org6bf16cd">
+<div id="outline-container-org796ce06" class="outline-3">
+<h3 id="org796ce06">2024-04-14</h3>
+<div class="outline-text-3" id="text-org796ce06">
 </div>
-<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">
+<div id="outline-container-org1198084" class="outline-4">
+<h4 id="org1198084">Uppgifter att räkna till nästa gång</h4>
+<div class="outline-text-4" id="text-org1198084">
 <p>
 12.2.1bf, 12.2.2cd, 12.2.3c, 12.2.11
 </p>
 </div>
 </div>
-<div id="outline-container-orgef7eb4d" class="outline-4">
-<h4 id="orgef7eb4d">Datorlaboration</h4>
-<div class="outline-text-4" id="text-orgef7eb4d">
+<div id="outline-container-org87e8642" class="outline-4">
+<h4 id="org87e8642">Datorlaboration</h4>
+<div class="outline-text-4" id="text-org87e8642">
 <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
@@ -395,21 +395,21 @@ gränsvärdet av a(k,m) då m går mot oändligheten?
 </div>
 </div>
 </div>
-<div id="outline-container-org4a80012" class="outline-3">
-<h3 id="org4a80012">2024-04-07</h3>
-<div class="outline-text-3" id="text-org4a80012">
+<div id="outline-container-orgff00c35" class="outline-3">
+<h3 id="orgff00c35">2024-04-07</h3>
+<div class="outline-text-3" id="text-orgff00c35">
 </div>
-<div id="outline-container-org3f1c3a4" class="outline-4">
-<h4 id="org3f1c3a4">Uppgifter att räkna till nästa gång</h4>
-<div class="outline-text-4" id="text-org3f1c3a4">
+<div id="outline-container-org10c6215" class="outline-4">
+<h4 id="org10c6215">Uppgifter att räkna till nästa gång</h4>
+<div class="outline-text-4" id="text-org10c6215">
 <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-orgd77ff3b" class="outline-4">
-<h4 id="orgd77ff3b">Beviset för kvadratisk reciprocitet</h4>
-<div class="outline-text-4" id="text-orgd77ff3b">
+<div id="outline-container-orgcb6d72a" class="outline-4">
+<h4 id="orgcb6d72a">Beviset för kvadratisk reciprocitet</h4>
+<div class="outline-text-4" id="text-orgcb6d72a">
 <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.
@@ -418,17 +418,17 @@ 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-orgb250740" class="outline-3">
-<h3 id="orgb250740">2024-04-02</h3>
-<div class="outline-text-3" id="text-orgb250740">
+<div id="outline-container-org84ac4df" class="outline-3">
+<h3 id="org84ac4df">2024-04-02</h3>
+<div class="outline-text-3" id="text-org84ac4df">
 <p>
 På fredag så räknar vi de uppgifter om diskreta logaritmer vi inte hann med förra gången.
 </p>
 </div>
 </div>
-<div id="outline-container-orged4ff0b" class="outline-3">
-<h3 id="orged4ff0b">2024-03-11</h3>
-<div class="outline-text-3" id="text-orged4ff0b">
+<div id="outline-container-orgecb5391" class="outline-3">
+<h3 id="orgecb5391">2024-03-11</h3>
+<div class="outline-text-3" id="text-orgecb5391">
 <p>
 Jag har nu bokat om föreläsningarna till Fredagar kl 13-15 (fortfarande i kompakta rummet)
 samt måndag 25 mars kl 13-15,
@@ -437,9 +437,9 @@ Det blir 10 tillfällen totalt, vilket bör räcka.
 </p>
 </div>
 </div>
-<div id="outline-container-org0de71ab" class="outline-3">
-<h3 id="org0de71ab">2024-03-06</h3>
-<div class="outline-text-3" id="text-org0de71ab">
+<div id="outline-container-orged53d50" class="outline-3">
+<h3 id="orged53d50">2024-03-06</h3>
+<div class="outline-text-3" id="text-orged53d50">
 <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.
@@ -448,9 +448,9 @@ Möjliga tider är måndag 25 mars kl 13-15, torsdag 25 april kl 13-15, måndag
 </p>
 </div>
 </div>
-<div id="outline-container-org84eda8d" class="outline-3">
-<h3 id="org84eda8d">2024-03-05</h3>
-<div class="outline-text-3" id="text-org84eda8d">
+<div id="outline-container-org69c699e" class="outline-3">
+<h3 id="org69c699e">2024-03-05</h3>
+<div class="outline-text-3" id="text-org69c699e">
 <p>
 Det har framförts önskemål om att byta tid för lektionerna i period 4 för att undvika
 kollision med kursen i optimeringslära.
@@ -471,9 +471,9 @@ Det rör sig om 11 tillfällen totalt.
 </p>
 </div>
 </div>
-<div id="outline-container-orgea6ed65" class="outline-3">
-<h3 id="orgea6ed65">2024-02-29</h3>
-<div class="outline-text-3" id="text-orgea6ed65">
+<div id="outline-container-org8b45b59" class="outline-3">
+<h3 id="org8b45b59">2024-02-29</h3>
+<div class="outline-text-3" id="text-org8b45b59">
 <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.
@@ -487,9 +487,9 @@ Till lektionen efter det (27 mars) så räknar ni
 </div>
 </div>
 
-<div id="outline-container-org823f5e2" class="outline-3">
-<h3 id="org823f5e2">2024-02-20</h3>
-<div class="outline-text-3" id="text-org823f5e2">
+<div id="outline-container-org6ee578d" class="outline-3">
+<h3 id="org6ee578d">2024-02-20</h3>
+<div class="outline-text-3" id="text-org6ee578d">
 <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.
@@ -500,7 +500,7 @@ grad 5 eller 6.
 </p>
 
 <div class="org-src-container">
-<pre class="src src-sage" id="orgce6ce24">def H_L_tree(f, p: int, r: int):
+<pre class="src src-sage" id="org2172c13">def H_L_tree(f, p: int, r: int):
 
     vert = [(0,0)]
     for j in range(1,r+1):
@@ -529,25 +529,25 @@ H_L_tree(f,p,r).plot(layout='tree')
 </div>
 
 
-<figure id="org4ce6b2f">
+<figure id="org81e109e">
 <img src="img/Henseluppgift.png" alt="Henseluppgift.png">
 
 </figure>
 </div>
 </div>
 
-<div id="outline-container-org1c24ff1" class="outline-3">
-<h3 id="org1c24ff1">2024-02-12</h3>
-<div class="outline-text-3" id="text-org1c24ff1">
+<div id="outline-container-org15914f2" class="outline-3">
+<h3 id="org15914f2">2024-02-12</h3>
+<div class="outline-text-3" id="text-org15914f2">
 <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-org499023d" class="outline-3">
-<h3 id="org499023d">2024-02-07</h3>
-<div class="outline-text-3" id="text-org499023d">
+<div id="outline-container-org445fa32" class="outline-3">
+<h3 id="org445fa32">2024-02-07</h3>
+<div class="outline-text-3" id="text-org445fa32">
 <p>
 Till nästa lektion (12 feb) så tittar ni på uppgifterna
 4.1.5, 4.1.9b, 4.2.8c,4.3.3.
@@ -557,9 +557,9 @@ att vara i Kompakta rummet.
 </div>
 </div>
 
-<div id="outline-container-orgf683b42" class="outline-3">
-<h3 id="orgf683b42">2024-01-30</h3>
-<div class="outline-text-3" id="text-orgf683b42">
+<div id="outline-container-org887cf9c" class="outline-3">
+<h3 id="org887cf9c">2024-01-30</h3>
+<div class="outline-text-3" id="text-org887cf9c">
 <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>
@@ -568,9 +568,9 @@ att vara i Kompakta rummet.
 </ul>
 </div>
 
-<div id="outline-container-org53dcc9b" class="outline-4">
-<h4 id="org53dcc9b">Tvillingfria primtal</h4>
-<div class="outline-text-4" id="text-org53dcc9b">
+<div id="outline-container-orge760dad" class="outline-4">
+<h4 id="orge760dad">Tvillingfria primtal</h4>
+<div class="outline-text-4" id="text-orge760dad">
 <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
@@ -578,7 +578,7 @@ garanterar oändligt många primtal i nZ + k.
 </p>
 
 <div class="org-src-container">
-<pre class="src src-sage" id="org400f273">def repr(n):
+<pre class="src src-sage" id="org173cf70">def repr(n):
     return [k for k in range(n) if gcd(k,n)==1]
 
 def isolated(n):
@@ -609,17 +609,17 @@ Körning visar att n=15, k=7 är minsta exemplet.
 </div>
 </div>
 
-<div id="outline-container-orgd22b4e6" class="outline-3">
-<h3 id="orgd22b4e6">2024-01-23</h3>
-<div class="outline-text-3" id="text-orgd22b4e6">
+<div id="outline-container-org488e68b" class="outline-3">
+<h3 id="org488e68b">2024-01-23</h3>
+<div class="outline-text-3" id="text-org488e68b">
 <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-org5900f63" class="outline-3">
-<h3 id="org5900f63">2024-01-16</h3>
-<div class="outline-text-3" id="text-org5900f63">
+<div id="outline-container-org96d1546" class="outline-3">
+<h3 id="org96d1546">2024-01-16</h3>
+<div class="outline-text-3" id="text-org96d1546">
 <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>
@@ -627,7 +627,7 @@ 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="#org7db4ce4">rekommenderade uppgifter</a>)
+(hämtade från listan med <a href="#org9bd3039">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.
@@ -641,19 +641,19 @@ till, nu med fokus på att förstå bevisen.</li>
 </div>
 </section>
 
-<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">
+<section id="outline-container-org7fb0ecc" class="outline-2">
+<h2 id="org7fb0ecc">Kurslitteratur <a id="org43c1e74"></a></h2>
+<div class="outline-text-2" id="text-org7fb0ecc">
 </div>
-<div id="outline-container-org09cac9a" class="outline-3">
-<h3 id="org09cac9a">Kursbok</h3>
-<div class="outline-text-3" id="text-org09cac9a">
+<div id="outline-container-org1046eac" class="outline-3">
+<h3 id="org1046eac">Kursbok</h3>
+<div class="outline-text-3" id="text-org1046eac">
 <p>
 Kursbok är <a href="https://www.prisjakt.nu/produkt.php?p=8083662">Elementary Number Theory</a> av Kenneth Rosen.
 </p>
 
 
-<figure id="org09cfcfd">
+<figure id="org2a1061a">
 <img src="img/Rosen6ed.png" alt="Rosen6ed.png" width="40%">
 
 <figcaption><span class="figure-number">Illustration 1 </span>Elementary Number Theory, Kenneth Rosen</figcaption>
@@ -665,13 +665,13 @@ vilket inte påverkar innehållet.
 </p>
 </div>
 </div>
-<div id="outline-container-orgdf2c024" class="outline-3">
-<h3 id="orgdf2c024">Bredvidläsning</h3>
-<div class="outline-text-3" id="text-orgdf2c024">
+<div id="outline-container-orgb1f71c0" class="outline-3">
+<h3 id="orgb1f71c0">Bredvidläsning</h3>
+<div class="outline-text-3" id="text-orgb1f71c0">
 </div>
-<div id="outline-container-org9934079" class="outline-4">
-<h4 id="org9934079">Fritt tillgängligt material</h4>
-<div class="outline-text-4" id="text-org9934079">
+<div id="outline-container-org1304ec9" class="outline-4">
+<h4 id="org1304ec9">Fritt tillgängligt material</h4>
+<div class="outline-text-4" id="text-org1304ec9">
 <p>
 Följande böcker är fritt tillgängliga på nätet. Kursboken är väldigt grundlig
 och täcker kursinnehållet, men det kan ändå vara bra att se olika
@@ -689,9 +689,9 @@ Jolly för en metod att hitta primitiva rötter.</li>
 </ul>
 </div>
 </div>
-<div id="outline-container-org486a906" class="outline-4">
-<h4 id="org486a906">Andra lämpliga böcker</h4>
-<div class="outline-text-4" id="text-org486a906">
+<div id="outline-container-org156f528" class="outline-4">
+<h4 id="org156f528">Andra lämpliga böcker</h4>
+<div class="outline-text-4" id="text-org156f528">
 <ul class="org-ul">
 <li>BAKER. A concise introduction to the theory of numbers.</li>
 <li>DAVENPORT. The higher arithmetic.</li>
@@ -711,13 +711,13 @@ fortbildning efter denna kurs.</li>
 
 
 
-<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">
+<section id="outline-container-org777e787" class="outline-2">
+<h2 id="org777e787">Kursinnehåll <a id="orgd3a32bb"></a></h2>
+<div class="outline-text-2" id="text-org777e787">
 </div>
-<div id="outline-container-org34795a7" class="outline-3">
-<h3 id="org34795a7">Avsnitt av kursboken</h3>
-<div class="outline-text-3" id="text-org34795a7">
+<div id="outline-container-org8bd2546" class="outline-3">
+<h3 id="org8bd2546">Avsnitt av kursboken</h3>
+<div class="outline-text-3" id="text-org8bd2546">
 <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
@@ -727,15 +727,15 @@ från just dessa avsnitt.
 </p>
 </div>
 
-<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 id="outline-container-org5c92b21" class="outline-4">
+<h4 id="org5c92b21">Rekommenderade uppgifter <a id="org9bd3039"></a></h4>
+<div class="outline-text-4" id="text-org5c92b21">
 </div>
 <ul class="org-ul">
-<li><a id="org15b8e33"></a>Kap 1<br>
+<li><a id="org180341a"></a>Kap 1<br>
 <ul class="org-ul">
-<li><a id="orgb33f2f0"></a>1.5<br>
-<div class="outline-text-6" id="text-orgb33f2f0">
+<li><a id="org7ad84d9"></a>1.5<br>
+<div class="outline-text-6" id="text-org7ad84d9">
 <p>
 8a,9b,18,36,37
 </p>
@@ -743,46 +743,46 @@ från just dessa avsnitt.
 </li>
 </ul>
 </li>
-<li><a id="org681038a"></a>Kap 3<br>
+<li><a id="org87a9a00"></a>Kap 3<br>
 <ul class="org-ul">
-<li><a id="org0f22bbf"></a>3.1<br>
-<div class="outline-text-6" id="text-org0f22bbf">
+<li><a id="org8d58eb7"></a>3.1<br>
+<div class="outline-text-6" id="text-org8d58eb7">
 <p>
 1ab, 2f,6.
 </p>
 </div>
 </li>
-<li><a id="orga37167f"></a>3.2<br>
-<div class="outline-text-6" id="text-orga37167f">
+<li><a id="org7773607"></a>3.2<br>
+<div class="outline-text-6" id="text-org7773607">
 <ol class="org-ol">
 <li></li>
 </ol>
 </div>
 </li>
-<li><a id="orgb03bced"></a>3.3<br>
-<div class="outline-text-6" id="text-orgb03bced">
+<li><a id="orgd200f28"></a>3.3<br>
+<div class="outline-text-6" id="text-orgd200f28">
 <p>
 1df,2ef,10,24,30,31
 </p>
 </div>
 </li>
-<li><a id="orgec1beae"></a>3.4<br>
-<div class="outline-text-6" id="text-orgec1beae">
+<li><a id="org5f021b7"></a>3.4<br>
+<div class="outline-text-6" id="text-org5f021b7">
 <p>
 1bc, 19*, 20*.
 </p>
 </div>
 </li>
-<li><a id="orgcb8a7bd"></a>3.5<br>
-<div class="outline-text-6" id="text-orgcb8a7bd">
+<li><a id="org54380bd"></a>3.5<br>
+<div class="outline-text-6" id="text-org54380bd">
 <p>
 1il, 2, 4c, 29cd,
   32*, 34, 58ac.
 </p>
 </div>
 </li>
-<li><a id="orga2dfbe1"></a>3.7<br>
-<div class="outline-text-6" id="text-orga2dfbe1">
+<li><a id="orge8d3c38"></a>3.7<br>
+<div class="outline-text-6" id="text-orge8d3c38">
 <p>
 1cd
 </p>
@@ -790,31 +790,31 @@ från just dessa avsnitt.
 </li>
 </ul>
 </li>
-<li><a id="org37c2a66"></a>Kap 4<br>
+<li><a id="org3c52ecc"></a>Kap 4<br>
 <ul class="org-ul">
-<li><a id="org6253340"></a>4.1<br>
-<div class="outline-text-6" id="text-org6253340">
+<li><a id="org60d0871"></a>4.1<br>
+<div class="outline-text-6" id="text-org60d0871">
 <p>
 4,5,7ab,9bc.
 </p>
 </div>
 </li>
-<li><a id="org54fbae8"></a>4.2<br>
-<div class="outline-text-6" id="text-org54fbae8">
+<li><a id="org6ccedb0"></a>4.2<br>
+<div class="outline-text-6" id="text-org6ccedb0">
 <p>
 1df, 8c, 9d.
 </p>
 </div>
 </li>
-<li><a id="org5ae1ea7"></a>4.3<br>
-<div class="outline-text-6" id="text-org5ae1ea7">
+<li><a id="org89b0458"></a>4.3<br>
+<div class="outline-text-6" id="text-org89b0458">
 <p>
 3,4.
 </p>
 </div>
 </li>
-<li><a id="org7fb6f3a"></a>4.4<br>
-<div class="outline-text-6" id="text-org7fb6f3a">
+<li><a id="orgce85497"></a>4.4<br>
+<div class="outline-text-6" id="text-orgce85497">
 <p>
 2ab.
 </p>
@@ -822,10 +822,10 @@ från just dessa avsnitt.
 </li>
 </ul>
 </li>
-<li><a id="org67c0b01"></a>Kap 5<br>
+<li><a id="orgce38e81"></a>Kap 5<br>
 <ul class="org-ul">
-<li><a id="org72b5624"></a>5.1<br>
-<div class="outline-text-6" id="text-org72b5624">
+<li><a id="org290a8f0"></a>5.1<br>
+<div class="outline-text-6" id="text-org290a8f0">
 <p>
 4ab.
 </p>
@@ -833,26 +833,26 @@ från just dessa avsnitt.
 </li>
 </ul>
 </li>
-<li><a id="org3e672b9"></a>Kap 6<br>
+<li><a id="org079c6dc"></a>Kap 6<br>
 <ul class="org-ul">
-<li><a id="org1f56359"></a>6.1<br>
-<div class="outline-text-6" id="text-org1f56359">
+<li><a id="org87f09e3"></a>6.1<br>
+<div class="outline-text-6" id="text-org87f09e3">
 <p>
 4,5,6,9,10,14,18,19,22,24,24,28,36,38*,41,48*,52.
 </p>
 </div>
 </li>
 
-<li><a id="org6facf0b"></a>6.2<br>
-<div class="outline-text-6" id="text-org6facf0b">
+<li><a id="orgbc16a8c"></a>6.2<br>
+<div class="outline-text-6" id="text-orgbc16a8c">
 <p>
 2,8,12,16ab.
 </p>
 </div>
 </li>
 
-<li><a id="org3eb9c1b"></a>6.3<br>
-<div class="outline-text-6" id="text-org3eb9c1b">
+<li><a id="orgffebf1d"></a>6.3<br>
+<div class="outline-text-6" id="text-orgffebf1d">
 <p>
 1d,6,7,22*
 </p>
@@ -861,31 +861,31 @@ från just dessa avsnitt.
 </ul>
 </li>
 
-<li><a id="orgdc43d50"></a>Kap 7<br>
+<li><a id="orgcfc4d04"></a>Kap 7<br>
 <ul class="org-ul">
-<li><a id="org70452c6"></a>7.1<br>
-<div class="outline-text-6" id="text-org70452c6">
+<li><a id="org614132a"></a>7.1<br>
+<div class="outline-text-6" id="text-org614132a">
 <p>
 2bc,5,8.
 </p>
 </div>
 </li>
-<li><a id="org613722d"></a>7.2<br>
-<div class="outline-text-6" id="text-org613722d">
+<li><a id="org871658a"></a>7.2<br>
+<div class="outline-text-6" id="text-org871658a">
 <p>
 1bd,2cd,8,34*,35,38*.
 </p>
 </div>
 </li>
-<li><a id="orgf2f87e9"></a>7.3<br>
-<div class="outline-text-6" id="text-orgf2f87e9">
+<li><a id="org122f2e6"></a>7.3<br>
+<div class="outline-text-6" id="text-org122f2e6">
 <p>
 3b,4,7,8,10,18,22**,28*,29cd.
 </p>
 </div>
 </li>
-<li><a id="org540c16c"></a>7.4<br>
-<div class="outline-text-6" id="text-org540c16c">
+<li><a id="org9ba696a"></a>7.4<br>
+<div class="outline-text-6" id="text-org9ba696a">
 <p>
 1bd,2be,14,22,23,24,30,31.
 </p>
@@ -894,47 +894,47 @@ från just dessa avsnitt.
 </ul>
 </li>
 
-<li><a id="orgd525786"></a>Kap 9<br>
+<li><a id="orgd9614bf"></a>Kap 9<br>
 <ul class="org-ul">
-<li><a id="org8894071"></a>9.1<br>
-<div class="outline-text-6" id="text-org8894071">
+<li><a id="org477479c"></a>9.1<br>
+<div class="outline-text-6" id="text-org477479c">
 <p>
  1ad, 2cd, 5b, 6df, 8, 10, 20*,
 22*.
 </p>
 </div>
 </li>
-<li><a id="org68316e6"></a>9.2<br>
-<div class="outline-text-6" id="text-org68316e6">
+<li><a id="orga68111e"></a>9.2<br>
+<div class="outline-text-6" id="text-orga68111e">
 <p>
 1d, 2d, 3e, 6.
 </p>
 </div>
 </li>
-<li><a id="orgabc73c3"></a>9.3<br>
-<div class="outline-text-6" id="text-orgabc73c3">
+<li><a id="orgf6dd661"></a>9.3<br>
+<div class="outline-text-6" id="text-orgf6dd661">
 <p>
 2,3c, 5c,6c, 8b, 10.
 </p>
 </div>
 </li>
-<li><a id="org63ae623"></a>9.4<br>
-<div class="outline-text-6" id="text-org63ae623">
+<li><a id="org37dfb2a"></a>9.4<br>
+<div class="outline-text-6" id="text-org37dfb2a">
 <p>
 1, 2b, 3a,
   4, 9, 10, 19, 20*.
 </p>
 </div>
 </li>
-<li><a id="org9c13bc0"></a>9.5<br>
-<div class="outline-text-6" id="text-org9c13bc0">
+<li><a id="org29656a1"></a>9.5<br>
+<div class="outline-text-6" id="text-org29656a1">
 <p>
 2,3,10.
 </p>
 </div>
 </li>
-<li><a id="org5015ce5"></a>9.6<br>
-<div class="outline-text-6" id="text-org5015ce5">
+<li><a id="orgf9dc898"></a>9.6<br>
+<div class="outline-text-6" id="text-orgf9dc898">
 <p>
 1bcg, 4def, 13*, 14*.
 </p>
@@ -943,31 +943,31 @@ från just dessa avsnitt.
 </ul>
 </li>
 
-<li><a id="org82f34bf"></a>Kap 11<br>
+<li><a id="org2d75d4e"></a>Kap 11<br>
 <ul class="org-ul">
-<li><a id="org3d2f276"></a>11.1<br>
-<div class="outline-text-6" id="text-org3d2f276">
+<li><a id="org762f628"></a>11.1<br>
+<div class="outline-text-6" id="text-org762f628">
 <p>
 1d, 4, 25.
 </p>
 </div>
 </li>
-<li><a id="orgc0c01e2"></a>11.2<br>
-<div class="outline-text-6" id="text-orgc0c01e2">
+<li><a id="orgd2d41f5"></a>11.2<br>
+<div class="outline-text-6" id="text-orgd2d41f5">
 <p>
 1cd, 2, 4, 5.
 </p>
 </div>
 </li>
-<li><a id="org1af5d6e"></a>11.3<br>
-<div class="outline-text-6" id="text-org1af5d6e">
+<li><a id="orgc0bf6e6"></a>11.3<br>
+<div class="outline-text-6" id="text-orgc0bf6e6">
 <p>
 1ef, 5, 6.
 </p>
 </div>
 </li>
-<li><a id="orgfe1e34d"></a>11.4<br>
-<div class="outline-text-6" id="text-orgfe1e34d">
+<li><a id="org53fd7ee"></a>11.4<br>
+<div class="outline-text-6" id="text-org53fd7ee">
 <p>
 1, 2, 5, 6.
 </p>
@@ -976,32 +976,32 @@ från just dessa avsnitt.
 </ul>
 </li>
 
-<li><a id="org2cc3178"></a>Kap 12<br>
+<li><a id="org4de3188"></a>Kap 12<br>
 <ul class="org-ul">
-<li><a id="org7cac01e"></a>12.2<br>
-<div class="outline-text-6" id="text-org7cac01e">
+<li><a id="org7b01410"></a>12.2<br>
+<div class="outline-text-6" id="text-org7b01410">
 <p>
 1bf, 2cd, 3c, 4c.
 </p>
 </div>
 </li>
-<li><a id="orgb90f3a1"></a>12.3<br>
-<div class="outline-text-6" id="text-orgb90f3a1">
+<li><a id="org1aa1c33"></a>12.3<br>
+<div class="outline-text-6" id="text-org1aa1c33">
 <p>
 1c, 2a, 6*, 7.
 </p>
 </div>
 </li>
-<li><a id="orgca93be0"></a>12.4<br>
-<div class="outline-text-6" id="text-orgca93be0">
+<li><a id="orgccd3c06"></a>12.4<br>
+<div class="outline-text-6" id="text-orgccd3c06">
 <p>
 1c, 2c, 3b, 4a,
   5b, 6b, 7b,  8, 10, 17.
 </p>
 </div>
 </li>
-<li><a id="org677f1bb"></a>12.5<br>
-<div class="outline-text-6" id="text-org677f1bb">
+<li><a id="org1a8a715"></a>12.5<br>
+<div class="outline-text-6" id="text-org1a8a715">
 <ol class="org-ol">
 <li></li>
 </ol>
@@ -1010,32 +1010,32 @@ från just dessa avsnitt.
 </ul>
 </li>
 
-<li><a id="orgedd8e06"></a>Kap 13<br>
+<li><a id="org919ec71"></a>Kap 13<br>
 <ul class="org-ul">
-<li><a id="orgbcdde20"></a>13.1<br>
-<div class="outline-text-6" id="text-orgbcdde20">
+<li><a id="org4beed34"></a>13.1<br>
+<div class="outline-text-6" id="text-org4beed34">
 <p>
 1, 2, 3, 8, 16.
 </p>
 </div>
 </li>
-<li><a id="org8e3a488"></a>13.2<br>
-<div class="outline-text-6" id="text-org8e3a488">
+<li><a id="org670cfbe"></a>13.2<br>
+<div class="outline-text-6" id="text-org670cfbe">
 <p>
 3, 4,
   6*, 8, 10, 11*, 20.
 </p>
 </div>
 </li>
-<li><a id="org528308d"></a>13.3<br>
-<div class="outline-text-6" id="text-org528308d">
+<li><a id="org9de6939"></a>13.3<br>
+<div class="outline-text-6" id="text-org9de6939">
 <p>
 1b, 2gh,3cd, 6, 7, 9c, 10ef.
 </p>
 </div>
 </li>
-<li><a id="orgf68bc5b"></a>13.4<br>
-<div class="outline-text-6" id="text-orgf68bc5b">
+<li><a id="org3183550"></a>13.4<br>
+<div class="outline-text-6" id="text-org3183550">
 <p>
 1c,
   2a, 3def, 4ab, 6de, 8*.
@@ -1045,25 +1045,25 @@ från just dessa avsnitt.
 </ul>
 </li>
 
-<li><a id="orgdcc1ad3"></a>Kap 14<br>
+<li><a id="org63d399d"></a>Kap 14<br>
 <ul class="org-ul">
-<li><a id="org59fea14"></a>14.1<br>
-<div class="outline-text-6" id="text-org59fea14">
+<li><a id="org85ae0e8"></a>14.1<br>
+<div class="outline-text-6" id="text-org85ae0e8">
 <p>
 1ac, 12, 13, 17a.
 </p>
 </div>
 </li>
-<li><a id="orgb5250d8"></a>14.2<br>
-<div class="outline-text-6" id="text-orgb5250d8">
+<li><a id="org3dd76f9"></a>14.2<br>
+<div class="outline-text-6" id="text-org3dd76f9">
 <p>
 16ab,
   17bc.
 </p>
 </div>
 </li>
-<li><a id="org3675a33"></a>14.3<br>
-<div class="outline-text-6" id="text-org3675a33">
+<li><a id="orgff2bf56"></a>14.3<br>
+<div class="outline-text-6" id="text-orgff2bf56">
 <p>
 1bc, 2c
 </p>
@@ -1075,15 +1075,15 @@ från just dessa avsnitt.
 </div>
 </div>
 
-<div id="outline-container-orgab0c2e2" class="outline-3">
-<h3 id="orgab0c2e2">Kort beskrivning av kursinnehållet</h3>
+<div id="outline-container-orgf97dd5f" class="outline-3">
+<h3 id="orgf97dd5f">Kort beskrivning av kursinnehållet</h3>
 </div>
 </section>
 
 
-<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">
+<section id="outline-container-orgb1afa66" class="outline-2">
+<h2 id="orgb1afa66">Föreläsningar <a id="org0da9d7f"></a></h2>
+<div class="outline-text-2" id="text-orgb1afa66">
 <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.
@@ -1262,9 +1262,9 @@ De svenska versionerna är nyare. Några av föreläsningarna tar två tillfäll
 </section>
 
 
-<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">
+<section id="outline-container-orgd9a1a3d" class="outline-2">
+<h2 id="orgd9a1a3d">Tentor <a id="org113b7d1"></a></h2>
+<div class="outline-text-2" id="text-orgd9a1a3d">
 <table>
 
 
@@ -1480,13 +1480,13 @@ De svenska versionerna är nyare. Några av föreläsningarna tar två tillfäll
 </section>
 
 
-<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">
+<section id="outline-container-orgaa8bfe8" class="outline-2">
+<h2 id="orgaa8bfe8">Datorlaborationer <a id="orgd7ec18a"></a></h2>
+<div class="outline-text-2" id="text-orgaa8bfe8">
 </div>
-<div id="outline-container-org7a98c02" class="outline-3">
-<h3 id="org7a98c02">SageMath</h3>
-<div class="outline-text-3" id="text-org7a98c02">
+<div id="outline-container-org0e9470f" class="outline-3">
+<h3 id="org0e9470f">SageMath</h3>
+<div class="outline-text-3" id="text-org0e9470f">
 <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>,
@@ -1502,9 +1502,9 @@ Ett tredje alternativ, enkelt och flärdfritt, är att mata in sin kod till <a h
 </p>
 </div>
 </div>
-<div id="outline-container-org38724a4" class="outline-3">
-<h3 id="org38724a4">Kod från vissa föreläsningar</h3>
-<div class="outline-text-3" id="text-org38724a4">
+<div id="outline-container-org4e01f4d" class="outline-3">
+<h3 id="org4e01f4d">Kod från vissa föreläsningar</h3>
+<div class="outline-text-3" id="text-org4e01f4d">
 <ul class="org-ul">
 <li><a href="labs/lecture0.html">Föreläsning 0</a></li>
 <li><a href="labs/lecture1.html">Föreläsning 1</a></li>
@@ -1515,21 +1515,21 @@ Ett tredje alternativ, enkelt och flärdfritt, är att mata in sin kod till <a h
 </ul>
 </div>
 </div>
-<div id="outline-container-org80ba8f8" class="outline-3">
-<h3 id="org80ba8f8">Laborationer</h3>
-<div class="outline-text-3" id="text-org80ba8f8">
+<div id="outline-container-org771ae33" class="outline-3">
+<h3 id="org771ae33">Laborationer</h3>
+<div class="outline-text-3" id="text-org771ae33">
 </div>
-<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">
+<div id="outline-container-orge16b88e" class="outline-4">
+<h4 id="orge16b88e">Hensellyft, Primitiva rötter, Kinesiska restsatsen</h4>
+<div class="outline-text-4" id="text-orge16b88e">
 <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-org4f8b714" class="outline-4">
-<h4 id="org4f8b714">Kedjebråk</h4>
-<div class="outline-text-4" id="text-org4f8b714">
+<div id="outline-container-org254ad94" class="outline-4">
+<h4 id="org254ad94">Kedjebråk</h4>
+<div class="outline-text-4" id="text-org254ad94">
 <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>
@@ -1540,20 +1540,20 @@ Finns att <a href="labs/kedjebraklab.html">läsa direkt</a> eller som <a href="l
 
 
 
-<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">
+<section id="outline-container-orgcab2c84" class="outline-2">
+<h2 id="orgcab2c84">Tidigare år <a id="org0573e61"></a></h2>
+<div class="outline-text-2" id="text-orgcab2c84">
 </div>
 
 
 
-<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 id="outline-container-org5db15ec" class="outline-3">
+<h3 id="org5db15ec">TATA54 Anteckningar från tidigare år</h3>
+<div class="outline-text-3" id="text-org5db15ec">
 </div>
-<div id="outline-container-org780ed90" class="outline-4">
-<h4 id="org780ed90">2023</h4>
-<div class="outline-text-4" id="text-org780ed90">
+<div id="outline-container-org2e74361" class="outline-4">
+<h4 id="org2e74361">2023</h4>
+<div class="outline-text-4" id="text-org2e74361">
 <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
@@ -1607,9 +1607,9 @@ tryckfel (skall vara w(d)). 7.2.38 är komplicerad och kan skippas.</li>
 </div>
 
 
-<div id="outline-container-org780092f" class="outline-4">
-<h4 id="org780092f">2021</h4>
-<div class="outline-text-4" id="text-org780092f">
+<div id="outline-container-org39f254e" class="outline-4">
+<h4 id="org39f254e">2021</h4>
+<div class="outline-text-4" id="text-org39f254e">
 <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
@@ -1657,9 +1657,9 @@ någon inbjudan, så mejla mig.</li>
 </div>
 </div>
 
-<div id="outline-container-org2b03280" class="outline-4">
-<h4 id="org2b03280">2020</h4>
-<div class="outline-text-4" id="text-org2b03280">
+<div id="outline-container-orgab915cd" class="outline-4">
+<h4 id="orgab915cd">2020</h4>
+<div class="outline-text-4" id="text-orgab915cd">
 <ul class="org-ul">
 <li><p>
 2020-12-12: Kursen kommer att ges VT2021, med start den 19e januari.
@@ -1712,9 +1712,9 @@ someone else (perhaps
 </div>
 </div>
 
-<div id="outline-container-org9b6101f" class="outline-4">
-<h4 id="org9b6101f">2019</h4>
-<div class="outline-text-4" id="text-org9b6101f">
+<div id="outline-container-org51934a3" class="outline-4">
+<h4 id="org51934a3">2019</h4>
+<div class="outline-text-4" id="text-org51934a3">
 <ul class="org-ul">
 <li>2019-11-01: The course will not be given spring 2020.</li>
 
@@ -1729,9 +1729,9 @@ available.</li>
 </div>
 </div>
 
-<div id="outline-container-orgba3d96f" class="outline-4">
-<h4 id="orgba3d96f">2018</h4>
-<div class="outline-text-4" id="text-orgba3d96f">
+<div id="outline-container-org51909e4" class="outline-4">
+<h4 id="org51909e4">2018</h4>
+<div class="outline-text-4" id="text-org51909e4">
 <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
@@ -1744,9 +1744,9 @@ available.</li>
 </div>
 </div>
 
-<div id="outline-container-org45290d5" class="outline-4">
-<h4 id="org45290d5">2017</h4>
-<div class="outline-text-4" id="text-org45290d5">
+<div id="outline-container-org50057cb" class="outline-4">
+<h4 id="org50057cb">2017</h4>
+<div class="outline-text-4" id="text-org50057cb">
 <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
@@ -1769,7 +1769,7 @@ Another text is <a href="https://wstein.org/ent/">Elementary Number Theory</a> a
 </ul>
 
 
-<figure id="org09a4929">
+<figure id="orgc676d9d">
 <img src="img/sieveE.jpg" alt="sieveE.jpg">
 
 </figure>
@@ -1779,9 +1779,9 @@ Another text is <a href="https://wstein.org/ent/">Elementary Number Theory</a> a
 </section>
 
 
-<section id="outline-container-org22888c0" class="outline-2">
-<h2 id="org22888c0">Index</h2>
-<div class="outline-text-2" id="text-org22888c0">
+<section id="outline-container-org27e935f" class="outline-2">
+<h2 id="org27e935f">Index</h2>
+<div class="outline-text-2" id="text-org27e935f">
 <p>
 <a href="sitemap.html">Samtliga nåbara filer</a>
 </p>
@@ -1790,7 +1790,7 @@ 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: 2024-08-22</p>
+<p class="date">Created: 2024-08-23</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 64e5f08..774907d 100644
--- a/public/sitemap.html
+++ b/public/sitemap.html
@@ -1,7 +1,7 @@
 <!DOCTYPE html>
 <html lang="en">
 <head>
-<!-- 2024-08-22 -->
+<!-- 2024-08-23 -->
 <meta charset="utf-8" />
 <meta name="viewport" content="width=device-width, initial-scale=1" />
 <title>Kurshemsida</title>
@@ -206,9 +206,11 @@
 <header>
 <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="senaste-nytt.html">senaste-nytt</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>
@@ -217,13 +219,11 @@
 <li><a href="labs/lecture0.html">lecture0</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="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: 2024-08-22</p>
+<p class="date">Created: 2024-08-23</p>
 <p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p>
 </footer>
 </body>
-- 
GitLab