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 $(n|p)\equiv n^{(p-1)/2}(modp)$ 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