diff --git a/TATA54/TENTOR/tenta-TATA54-20240601-losning.log b/TATA54/TENTOR/tenta-TATA54-20240601-losning.log index 0bafbd881b2747c50d53f5c9e9c652ee2bf31213..af47e1e547b9d722f041c183205932594af47627 100644 --- a/TATA54/TENTOR/tenta-TATA54-20240601-losning.log +++ b/TATA54/TENTOR/tenta-TATA54-20240601-losning.log @@ -1,4 +1,4 @@ -This is pdfTeX, Version 3.141592653-2.6-1.40.26 (TeX Live 2024/TeX Live for SUSE Linux) (preloaded format=pdflatex 2024.4.2) 22 MAY 2024 11:13 +This is pdfTeX, Version 3.141592653-2.6-1.40.26 (TeX Live 2024/TeX Live for SUSE Linux) (preloaded format=pdflatex 2024.4.2) 4 JUN 2024 10:32 entering extended mode restricted \write18 enabled. file:line:error style messages enabled. @@ -227,7 +227,7 @@ pfb></usr/share/texmf/fonts/type1/public/amsfonts/cm/cmr10.pfb></usr/share/texm f/fonts/type1/public/amsfonts/cm/cmr17.pfb></usr/share/texmf/fonts/type1/public /amsfonts/cm/cmr8.pfb></usr/share/texmf/fonts/type1/public/amsfonts/cm/cmsy10.p fb></usr/share/texmf/fonts/type1/public/amsfonts/cm/cmsy8.pfb> -Output written on tenta-TATA54-20240601-losning.pdf (2 pages, 106733 bytes). +Output written on tenta-TATA54-20240601-losning.pdf (2 pages, 106721 bytes). PDF statistics: 56 PDF objects out of 1000 (max. 8388607) 33 compressed objects within 1 object stream diff --git a/TATA54/TENTOR/tenta-TATA54-20240601-losning.pdf b/TATA54/TENTOR/tenta-TATA54-20240601-losning.pdf index 5dfe39ca43f50cbe0f238abf2c894abe9cd7f152..264f94bb4f8119221d19f600939bca998514b80b 100644 Binary files a/TATA54/TENTOR/tenta-TATA54-20240601-losning.pdf and b/TATA54/TENTOR/tenta-TATA54-20240601-losning.pdf differ diff --git a/TATA54/TENTOR/tenta-TATA54-20240601-losning.synctex.gz b/TATA54/TENTOR/tenta-TATA54-20240601-losning.synctex.gz index 60b34a4d2a0ddcd9e3f212e9ad3b7d7d6873a06c..05153b063b1aaa3e42716e49d940c9c6ca79f2b0 100644 Binary files a/TATA54/TENTOR/tenta-TATA54-20240601-losning.synctex.gz and b/TATA54/TENTOR/tenta-TATA54-20240601-losning.synctex.gz differ diff --git a/TATA54/TENTOR/tenta-TATA54-20240601-losning.tex b/TATA54/TENTOR/tenta-TATA54-20240601-losning.tex index ed0c3b14ea86eb7cde2ee43c6af1e3d8a5c72d4d..0277b6d85df947145de7d737545272857db82f48 100644 --- a/TATA54/TENTOR/tenta-TATA54-20240601-losning.tex +++ b/TATA54/TENTOR/tenta-TATA54-20240601-losning.tex @@ -37,7 +37,7 @@ Examinator: Jan Snellman} så det har nollställena 0,1,-1 modulo 3. Den formella derivatan är \(f'(x)=5x^4+2\), så \(f'(x) \equiv -(x^4+1) \mod 3\). - Alltså är \(f'(x)\) konstant noll evaluerat på \(\Z_{3}\). + Alltså är \(f'(x)\) alltid nollskiljd evaluerat på \(\Z_{3}\). Vidare: enligt Hensels lemma så lyfter dessa tre nollställen unikt till nollställen modulo \(3^k\), för \(k \ge 2\). diff --git a/homepage/exams/2024/tenta-TATA54-20240601-losning.pdf b/homepage/exams/2024/tenta-TATA54-20240601-losning.pdf index 5dfe39ca43f50cbe0f238abf2c894abe9cd7f152..264f94bb4f8119221d19f600939bca998514b80b 100644 Binary files a/homepage/exams/2024/tenta-TATA54-20240601-losning.pdf and b/homepage/exams/2024/tenta-TATA54-20240601-losning.pdf differ diff --git a/public/exams/2024/tenta-TATA54-20240601-losning.pdf b/public/exams/2024/tenta-TATA54-20240601-losning.pdf index 5dfe39ca43f50cbe0f238abf2c894abe9cd7f152..264f94bb4f8119221d19f600939bca998514b80b 100644 Binary files a/public/exams/2024/tenta-TATA54-20240601-losning.pdf and b/public/exams/2024/tenta-TATA54-20240601-losning.pdf differ diff --git a/public/sitemap.html b/public/sitemap.html index 7e79e130b92be80dcf7c074fe33573cff1cdc963..418287e0df14cdb98552e56258bf7cf4e491b2ed 100644 --- a/public/sitemap.html +++ b/public/sitemap.html @@ -1,7 +1,7 @@ <!DOCTYPE html> <html lang="en"> <head> -<!-- 2024-06-01 --> +<!-- 2024-06-04 --> <meta charset="utf-8" /> <meta name="viewport" content="width=device-width, initial-scale=1" /> <title>Kurshemsida</title> @@ -223,7 +223,7 @@ </main> <footer id="postamble" class="status"> <p class="author">Author: Jan Snellman</p> -<p class="date">Created: 2024-06-01</p> +<p class="date">Created: 2024-06-04</p> <p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p> </footer> </body>