 Quadratic residue

For an odd prime $p$, a nonzero class $a$ is a quadratic residue when $a\equiv x^2(\mathrm{mod}p)$. These residues form an index-two subgroup of $(\mathbb{Z}/p\mathbb{Z}{)}^{\times }$.

A quadratic residue is a concept from number theory, particularly in the study of modular arithmetic.