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Commit 4020669c authored by Jan Snellman's avatar Jan Snellman
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lösning u 1 fixad

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Output written on tenta-TATA54-20240601-losning.pdf (2 pages, 106733 bytes).
Output written on tenta-TATA54-20240601-losning.pdf (2 pages, 106721 bytes).
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......@@ -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 \(k \ge 2\).
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<!-- 2024-06-01 -->
<!-- 2024-06-04 -->
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<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>
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