Modular Arithmetic/Quadratic Residues

Quadratic Residue

An integer $\alpha$ may be called a quadratic residue modulo $\beta$ if there exists an integer, $\gamma$, such that the congruence,

$\alpha \equiv \gamma ^{2}{\pmod {\beta }}$

holds. Else $\alpha$ is a quadratic nonresidue modulo $\beta$.