A residue of order 2. A number $a$ for which the congruence $x^2 ≡ a \pmod m$ has a solution is called a quadratic residue modulo $m$.

A residue of order 2. A number $a$ for which the congruence $x^2 ≡ a \pmod m$ has a solution is called a quadratic residue modulo $m$; in other words, $a$ is a quadratic residue modulo $m$ if for a certain integer $x$ the number $x^2 − a$ is divisible by $m$; if this congruence has no solution, then $a$ is called a quadratic nonresidue.