PlanetMath: Euler's criterion

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Euler's criterion

(Theorem)

Let be an odd prime and an integer such that (that is, and are relatively prime).

Then $(n\vert p)\equiv n^{(p-1)/2}\pmod{p}$ where $(n\vert p)$ is the Legendre symbol.

"Euler's criterion" is owned by drini. [ owner history (1) ]

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Cross-references: Legendre symbol, relatively prime, integer, prime, odd
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This is version 2 of Euler's criterion, born on 2002-02-15, modified 2003-01-24.
Object id is 1965, canonical name is EulersCriterion.
Accessed 6210 times total.

Classification:

11A15 (Number theory :: Elementary number theory :: Power residues, reciprocity)

Pending Errata and Addenda

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