result on quadratic residues

Theorem. Let p be an odd prime. Then -3 is a quadratic residueMathworldPlanetmath modulo p if and only if p1(mod3).

Proof. Preliminary to the proof, we remark first that -1 is a quadratic residue modulo p, where p is an odd prime, if and only if p1(mod4).

If p1(mod4) then


Now if p3(mod4), then


Thus, (-3p)=(p3), and (p3)=1 if and only if p1(mod3).

Title result on quadratic residues
Canonical name ResultOnQuadraticResidues
Date of creation 2013-03-22 16:08:09
Last modified on 2013-03-22 16:08:09
Owner gilbert_51126 (14238)
Last modified by gilbert_51126 (14238)
Numerical id 25
Author gilbert_51126 (14238)
Entry type Theorem
Classification msc 11-00