https://www.rieselprime.de/z/index.php?title=Law_of_quadratic_reciprocity&feed=atom&action=history
Law of quadratic reciprocity - Revision history
2024-03-28T23:36:33Z
Revision history for this page on the wiki
MediaWiki 1.31.1
https://www.rieselprime.de/z/index.php?title=Law_of_quadratic_reciprocity&diff=26350&oldid=prev
Happy5214: Moving to new subcategory
2022-10-02T18:19:51Z
<p>Moving to new subcategory</p>
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<td colspan="2" style="background-color: #fff; color: #222; text-align: center;">Revision as of 18:19, 2 October 2022</td>
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<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>*[[Wikipedia:Quadratic_reciprocity|Wikipedia]]</div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>*[[Wikipedia:Quadratic_reciprocity|Wikipedia]]</div></td></tr>
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Happy5214
https://www.rieselprime.de/z/index.php?title=Law_of_quadratic_reciprocity&diff=12198&oldid=prev
Happy5214: Enclosing remaining variable in <math> tag and linking person
2020-10-26T20:15:45Z
<p>Enclosing remaining variable in <math> tag and linking person</p>
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<td colspan="2" style="background-color: #fff; color: #222; text-align: center;">Revision as of 20:15, 26 October 2020</td>
</tr><tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l1" >Line 1:</td>
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<tr><td class='diff-marker'>−</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>The '''law of quadratic reciprocity''' predicts whether an odd [[prime]] number <del class="diffchange diffchange-inline">''</del>p<del class="diffchange diffchange-inline">'' </del>is a [[quadratic residue]] or non-residue modulo another odd prime number <math>q</math> if we know whether <math>q</math> is a quadratic residue or non-residue modulo <math>p</math>.</div></td><td class='diff-marker'>+</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>The '''law of quadratic reciprocity''' predicts whether an odd [[prime]] number <ins class="diffchange diffchange-inline"><math></ins>p<ins class="diffchange diffchange-inline"></math> </ins>is a [[quadratic residue]] or non-residue modulo another odd prime number <math>q</math> if we know whether <math>q</math> is a quadratic residue or non-residue modulo <math>p</math>.</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>*If at least one of <math>p</math> or <math>q</math> are congruent to 1 mod 4: <math>p</math> is a quadratic residue modulo <math>q</math> if and only if <math>q</math> is a quadratic residue modulo <math>p</math>.</div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>*If at least one of <math>p</math> or <math>q</math> are congruent to 1 mod 4: <math>p</math> is a quadratic residue modulo <math>q</math> if and only if <math>q</math> is a quadratic residue modulo <math>p</math>.</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>*If both of <math>p</math> or <math>q</math> are congruent to 3 mod 4: <math>p</math> is a quadratic residue modulo <math>q</math> if and only if <math>q</math> is a quadratic non-residue modulo <math>p</math>.</div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>*If both of <math>p</math> or <math>q</math> are congruent to 3 mod 4: <math>p</math> is a quadratic residue modulo <math>q</math> if and only if <math>q</math> is a quadratic non-residue modulo <math>p</math>.</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td></tr>
<tr><td class='diff-marker'>−</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>This theorem was first proved by Carl Friedrich Gauss in 1801.</div></td><td class='diff-marker'>+</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>This theorem was first proved by <ins class="diffchange diffchange-inline">[[</ins>Carl Friedrich Gauss<ins class="diffchange diffchange-inline">]] </ins>in 1801.</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>This does not cover the cases where we want to know whether -1 or 2 are quadratic residues or non-residues modulo <math>p</math>.</div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>This does not cover the cases where we want to know whether -1 or 2 are quadratic residues or non-residues modulo <math>p</math>.</div></td></tr>
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Happy5214
https://www.rieselprime.de/z/index.php?title=Law_of_quadratic_reciprocity&diff=837&oldid=prev
Karbon at 10:40, 6 February 2019
2019-02-06T10:40:29Z
<p></p>
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<td colspan="2" style="background-color: #fff; color: #222; text-align: center;">Revision as of 10:40, 6 February 2019</td>
</tr><tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l1" >Line 1:</td>
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<tr><td class='diff-marker'>−</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>The '''law of quadratic reciprocity''' predicts whether an odd [[prime <del class="diffchange diffchange-inline">number</del>]] ''p'' is a [[quadratic residue]] or non-residue modulo another odd prime number <math>q</math> if we know whether <math>q</math> is a quadratic residue or non-residue modulo <math>p</math>.</div></td><td class='diff-marker'>+</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>The '''law of quadratic reciprocity''' predicts whether an odd [[prime]] <ins class="diffchange diffchange-inline">number </ins>''p'' is a [[quadratic residue]] or non-residue modulo another odd prime number <math>q</math> if we know whether <math>q</math> is a quadratic residue or non-residue modulo <math>p</math>.</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>*If at least one of <math>p</math> or <math>q</math> are congruent to 1 mod 4: <math>p</math> is a quadratic residue modulo <math>q</math> if and only if <math>q</math> is a quadratic residue modulo <math>p</math>.</div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>*If at least one of <math>p</math> or <math>q</math> are congruent to 1 mod 4: <math>p</math> is a quadratic residue modulo <math>q</math> if and only if <math>q</math> is a quadratic residue modulo <math>p</math>.</div></td></tr>
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<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>==External links==</div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>==External links==</div></td></tr>
<tr><td class='diff-marker'>−</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>*[<del class="diffchange diffchange-inline">https</del>:<del class="diffchange diffchange-inline">//en.wikipedia.org/wiki/</del>Quadratic_reciprocity Wikipedia]</div></td><td class='diff-marker'>+</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>*[<ins class="diffchange diffchange-inline">[Wikipedia</ins>:Quadratic_reciprocity<ins class="diffchange diffchange-inline">|</ins>Wikipedia<ins class="diffchange diffchange-inline">]</ins>]</div></td></tr>
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Karbon
https://www.rieselprime.de/z/index.php?title=Law_of_quadratic_reciprocity&diff=535&oldid=prev
Karbon: restored
2019-01-26T22:45:10Z
<p>restored</p>
<p><b>New page</b></p><div>The '''law of quadratic reciprocity''' predicts whether an odd [[prime number]] ''p'' is a [[quadratic residue]] or non-residue modulo another odd prime number <math>q</math> if we know whether <math>q</math> is a quadratic residue or non-residue modulo <math>p</math>.<br />
<br />
*If at least one of <math>p</math> or <math>q</math> are congruent to 1 mod 4: <math>p</math> is a quadratic residue modulo <math>q</math> if and only if <math>q</math> is a quadratic residue modulo <math>p</math>.<br />
*If both of <math>p</math> or <math>q</math> are congruent to 3 mod 4: <math>p</math> is a quadratic residue modulo <math>q</math> if and only if <math>q</math> is a quadratic non-residue modulo <math>p</math>.<br />
<br />
This theorem was first proved by Carl Friedrich Gauss in 1801.<br />
<br />
This does not cover the cases where we want to know whether -1 or 2 are quadratic residues or non-residues modulo <math>p</math>.<br />
<br />
*2 is a quadratic residue modulo <math>p</math> if and only if <math>p</math> is congruent to 1 or 7 (mod 8).<br />
*-1 is a quadratic residue modulo <math>p</math> if and only if <math>p</math> is congruent to 1 (mod 4).<br />
<br />
==External links==<br />
*[https://en.wikipedia.org/wiki/Quadratic_reciprocity Wikipedia]<br />
[[Category:Math]]</div>
Karbon