In number theory, the law of quadratic reciprocity is a theorem about modular arithmetic that gives conditions for the solvability of quadratic equations modulo prime numbers. (Ref: http://en.m.wikipedia.org/wiki/Quadratic_reciprocity)

In number theory, the law of quadratic reciprocity is a theorem about modular arithmetic that gives conditions for the solvability of quadratic equations modulo prime numbers. Reference: Wikipedia

The theorem was conjectured by Euler and Legendre and first proven by Gauss. He refers to it as the "fundamental theorem" in the "Disquisitiones Arithmeticae".