Legendre symbol

Legendre SymbolDlmfMathworldPlanetmath.
Let p be an odd prime. The Legendre symbol (ap) or (a|p) is defined as:

(ap)={1if a is a quadratic residue (modp)-1if a is a quadratic nonresidue (modp)0if p divides a

The Legendre symbol can be computed by means of Euler’s criterion or Gauss’ lemma.

GeneralizationsPlanetmathPlanetmath of this symbol are the Jacobi SymbolDlmfMathworldPlanetmath and the Kronecker symbolMathworldPlanetmath.

Title Legendre symbol
Canonical name LegendreSymbol
Date of creation 2013-03-22 11:44:46
Last modified on 2013-03-22 11:44:46
Owner alozano (2414)
Last modified by alozano (2414)
Numerical id 15
Author alozano (2414)
Entry type Definition
Classification msc 11-00
Classification msc 97U20
Related topic JacobiSymbol
Related topic EulersCriterion
Related topic QuadraticResidue
Related topic KroneckerSymbol
Related topic QuadraticReciprocityRule
Related topic QuadraticCongruence