Category:Definitions/Quadratic Residues

This category contains definitions related to Quadratic Residues.
Related results can be found in Category:Quadratic Residues.

Let $p$ be an odd prime.

Let $a \in \Z$ be an integer such that $a \not \equiv 0 \pmod p$.

Then $a$ is a quadratic residue of $p$ if and only if $x^2 \equiv a \pmod p$ has a solution.

That is, if and only if:

$\exists x \in \Z: x^2 \equiv a \pmod p$