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单词 LegendreSymbol
释义

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.

TitleLegendre symbol
Canonical nameLegendreSymbol
Date of creation2013-03-22 11:44:46
Last modified on2013-03-22 11:44:46
Owneralozano (2414)
Last modified byalozano (2414)
Numerical id15
Authoralozano (2414)
Entry typeDefinition
Classificationmsc 11-00
Classificationmsc 97U20
Related topicJacobiSymbol
Related topicEulersCriterion
Related topicQuadraticResidue
Related topicKroneckerSymbol
Related topicQuadraticReciprocityRule
Related topicQuadraticCongruence
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更新时间:2025/5/4 14:25:20