# Euler’s criterion

Let $p$ be an odd prime and $n$ an integer such that $(n,p)=1$ (that is, $n$ and $p$ are relatively prime).

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

 Title Euler’s criterion Canonical name EulersCriterion Date of creation 2013-03-22 12:20:00 Last modified on 2013-03-22 12:20:00 Owner drini (3) Last modified by drini (3) Numerical id 5 Author drini (3) Entry type Theorem Classification msc 11A15 Related topic GaussLemma Related topic QuadraticReciprocityRule Related topic LegendreSymbol Related topic QuadraticResidue Related topic ProofOfGaussLemma Related topic PropertiesOfTheLegendreSymbol Related topic 1IsQuadraticResidueIfAndOnlyIfPequiv1Mod4