Congruence condition for two to be a quadratic residue

Statement

Suppose $p$ is an odd prime. Then:

$2$ is a quadratic residue modulo $p$ if and only if $p\equiv \pm 1{\pmod {8}}$ , i.e., $p\equiv 1{\pmod {8}}$ or $p\equiv 7{\pmod {8}}$ .
$2$ is a quadratic nonresidue modulo $p$ if and only if $p\equiv \pm 3{\pmod {8}}$ , i.e, $p\equiv 3{\pmod {8}}$ or $p\equiv 5{\pmod {8}}$ .