Definition:Legendre Symbol/Definition 2

Definition
Let $p$ be an odd prime.

Let $a \in \Z$.

The Legendre symbol $\paren {\dfrac a p}$ is defined as:
 * $0 \quad$ if $a \equiv 0 \pmod p$
 * $+1 \quad$ if $a$ is a quadratic residue of $p$
 * $-1 \quad$ if $a$ is a quadratic non-residue of $p$

Also see

 * Equivalence of Definitions of Legendre Symbol