http://wiki.sommarmatte.se/wikis/forberedandematte/index.php?action=history&feed=atom&title=L%C3%B6sning_1.4.1.b 2026-07-04T20:48:33Z Versionshistorik för denna sida på wikin MediaWiki 1.11.1 http://wiki.sommarmatte.se/wikis/forberedandematte/index.php?title=L%C3%B6sning_1.4.1.b&diff=741&oldid=prev 2012-06-20T12:33:38Z

<p></p> <table style="background-color: white; color:black;"> <col class='diff-marker' /> <col class='diff-content' /> <col class='diff-marker' /> <col class='diff-content' /> <tr> <td colspan='2' style="background-color: white; color:black;">← Äldre version</td> <td colspan='2' style="background-color: white; color:black;">Versionen från 20 juni 2012 kl. 12.33</td> </tr> <tr><td colspan="2" class="diff-lineno">Rad 1:</td> <td colspan="2" class="diff-lineno">Rad 1:</td></tr> <tr><td class='diff-marker'>-</td><td style="background: #ffa; color:black; font-size: smaller;"><div>Om vi räknar modulo 10 får vi att &lt;math&gt;37^120\<del style="color: red; font-weight: bold; text-decoration: none;">equiv_{10}</del>7^120\<del style="color: red; font-weight: bold; text-decoration: none;">equiv_{10}</del>(7^2)^{60}\<del style="color: red; font-weight: bold; text-decoration: none;">equiv_{10}</del>49^{60}\<del style="color: red; font-weight: bold; text-decoration: none;">equiv_{10}</del>9^{60}\<del style="color: red; font-weight: bold; text-decoration: none;">equiv_{10}</del>(9^2)^{30} <del style="color: red; font-weight: bold; text-decoration: none;">&lt;/math&gt;</del></div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div>Om vi räknar modulo <ins style="color: red; font-weight: bold; text-decoration: none;">&lt;math&gt;</ins>10<ins style="color: red; font-weight: bold; text-decoration: none;">&lt;/math&gt; </ins>får vi att</div></td></tr> <tr><td class='diff-marker'>-</td><td style="background: #ffa; color:black; font-size: smaller;"><div><del style="color: red; font-weight: bold; text-decoration: none;">&lt;math&gt;</del></div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div>&#160;</div></td></tr> <tr><td class='diff-marker'>-</td><td style="background: #ffa; color:black; font-size: smaller;"><div>\<del style="color: red; font-weight: bold; text-decoration: none;">equiv_{10}</del>81^{30}\<del style="color: red; font-weight: bold; text-decoration: none;">equiv_{10} </del>1^{30}\<del style="color: red; font-weight: bold; text-decoration: none;">equiv_</del>{10}<del style="color: red; font-weight: bold; text-decoration: none;">1</del>&lt;/math&gt;<del style="color: red; font-weight: bold; text-decoration: none;">, </del>så entalssiffran är en etta.</div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div>&lt;math&gt;<ins style="color: red; font-weight: bold; text-decoration: none;">\begin{align} </ins>37^<ins style="color: red; font-weight: bold; text-decoration: none;">{</ins>120<ins style="color: red; font-weight: bold; text-decoration: none;">}&amp;</ins>\<ins style="color: red; font-weight: bold; text-decoration: none;">equiv </ins>7^<ins style="color: red; font-weight: bold; text-decoration: none;">{</ins>120<ins style="color: red; font-weight: bold; text-decoration: none;">}</ins>\<ins style="color: red; font-weight: bold; text-decoration: none;">equiv </ins>(7^2)^{60}\<ins style="color: red; font-weight: bold; text-decoration: none;">equiv </ins>49^{60}\<ins style="color: red; font-weight: bold; text-decoration: none;">equiv\\&amp;\equiv </ins>9^{60}\<ins style="color: red; font-weight: bold; text-decoration: none;">equiv </ins>(9^2)^{30}\<ins style="color: red; font-weight: bold; text-decoration: none;">equiv </ins>81^{30}\<ins style="color: red; font-weight: bold; text-decoration: none;">equiv </ins>1^{30}\<ins style="color: red; font-weight: bold; text-decoration: none;">equiv 1\pmod</ins>{10}<ins style="color: red; font-weight: bold; text-decoration: none;">\end{align}</ins>&lt;/math&gt;</div></td></tr> <tr><td colspan="2">&nbsp;</td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div>&#160;</div></td></tr> <tr><td colspan="2">&nbsp;</td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div>så entalssiffran är en etta.</div></td></tr> </table>

Samuel http://wiki.sommarmatte.se/wikis/forberedandematte/index.php?title=L%C3%B6sning_1.4.1.b&diff=421&oldid=prev 2012-06-11T11:47:25Z

<p></p> <table style="background-color: white; color:black;"> <col class='diff-marker' /> <col class='diff-content' /> <col class='diff-marker' /> <col class='diff-content' /> <tr> <td colspan='2' style="background-color: white; color:black;">← Äldre version</td> <td colspan='2' style="background-color: white; color:black;">Versionen från 11 juni 2012 kl. 11.47</td> </tr> <tr><td colspan="2" class="diff-lineno">Rad 1:</td> <td colspan="2" class="diff-lineno">Rad 1:</td></tr> <tr><td class='diff-marker'>-</td><td style="background: #ffa; color:black; font-size: smaller;"><div>Om vi räknar modulo 10 får vi att &lt;math&gt;37^120\equiv_{10}7^120\equiv_{10}(7^2)^{60}\equiv_{10}49^{60}\equiv_{10}9^{60}\equiv_{10}(9^2)^{30}\equiv_{10}81^{30}\equiv_{10} 1^{30}\equiv_{10}1&lt;/math&gt;, så entalssiffran är en etta.</div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div>Om vi räknar modulo 10 får vi att &lt;math&gt;37^120\equiv_{10}7^120\equiv_{10}(7^2)^{60}\equiv_{10}49^{60}\equiv_{10}9^{60}\equiv_{10}(9^2)^{30} <ins style="color: red; font-weight: bold; text-decoration: none;">&lt;/math&gt;</ins></div></td></tr> <tr><td colspan="2">&nbsp;</td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;">&lt;math&gt;</ins></div></td></tr> <tr><td colspan="2">&nbsp;</td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div>\equiv_{10}81^{30}\equiv_{10} 1^{30}\equiv_{10}1&lt;/math&gt;, så entalssiffran är en etta.</div></td></tr> </table>

Samuel http://wiki.sommarmatte.se/wikis/forberedandematte/index.php?title=L%C3%B6sning_1.4.1.b&diff=420&oldid=prev 2012-06-11T11:43:53Z

<p>Ny sida: Om vi räknar modulo 10 får vi att &lt;math&gt;37^120\equiv_{10}7^120\equiv_{10}(7^2)^{60}\equiv_{10}49^{60}\equiv_{10}9^{60}\equiv_{10}(9^2)^{30}\equiv_{10}81^{30}\equiv_{10} 1^{30}\equiv_{10}1...</p> <p><b>Ny sida</b></p><div>Om vi räknar modulo 10 får vi att &lt;math&gt;37^120\equiv_{10}7^120\equiv_{10}(7^2)^{60}\equiv_{10}49^{60}\equiv_{10}9^{60}\equiv_{10}(9^2)^{30}\equiv_{10}81^{30}\equiv_{10} 1^{30}\equiv_{10}1&lt;/math&gt;, så entalssiffran är en etta.</div>

Samuel