In mathematics, a number q is called a quadratic residue modulo p if there exists an integer x such that:

${x^2}\equiv{q}\ (mod\ p)$

Otherwise, q is called a quadratic non-residue.

In effect, a quadratic residue modulo p is a number that has a square root in modular arithmetic when the modulus is p. The law of quadratic reciprocity says something about quadratic residues and primes.