https://www.ellipticcurve.info/Legendre_symbol/history?feed=atomLegendre symbol - Revision history2026-05-06T10:34:25ZRevision history for this page on the wikiMediaWiki 1.42.3https://www.ellipticcurve.info/index.php?title=Legendre_symbol&diff=289&oldid=prevRational Point: def2025-01-12T12:48:36Z<p>def</p>
<p><b>New page</b></p><div>== Legendre symbols ==<br />
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The '''Legendre symbol''' of an integer ''a'' over an odd prime ''p'' is defined<br />
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:<math>\left({a\over p}\right)\cong a^\frac{p-1}2\mod p;</math><br />
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:<math>\left({a\over p}\right)\in\{-1,0,1\}.</math><br />
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== Euler’s criterion ==<br />
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By [[Fermat’s little theorem]] we have<br />
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:<math>a^p\cong a\mod p</math><br />
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and if ''a'' is not divisible by the odd prime ''p'', then<br />
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:<math>a^{p-1}\cong 1\mod p.</math><br />
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To be continued ...</div>Rational Point