quadratic reciprocity rule

Theorem (Law of Quadratic Reciprocity).

Let p and q be two distinct odd primes. Then:


where () is the Jacobi (http://planetmath.org/JacobiSymbol) symbol (or Legendre symbolMathworldPlanetmath).

The following is an equivalentMathworldPlanetmathPlanetmathPlanetmathPlanetmath formulation of the Law of Quadratic Reciprocity:

Theorem (Quadratic Reciprocity (second form)).

Let p,q be distinct odd primes. Then:

  1. 1.

    (pq)=(qp) if one of p or q is congruentMathworldPlanetmath to 1 modulo 4;

  2. 2.

    (pq)=-(qp) if both p and q are congruent to 3 modulo 4.

Title quadratic reciprocity rule
Canonical name QuadraticReciprocityRule
Date of creation 2013-03-22 11:42:27
Last modified on 2013-03-22 11:42:27
Owner alozano (2414)
Last modified by alozano (2414)
Numerical id 33
Author alozano (2414)
Entry type Theorem
Classification msc 11A15
Synonym quadratic reciprocity
Related topic EulersCriterion
Related topic CubicReciprocityLaw
Related topic QuadraticReciprocityForPolynomials
Related topic LegendreSymbol