Definition:Legendre Symbol/Definition 1

Definition
Let $p$ be an odd prime.

Let $a \in \Z$.

The Legendre symbol $\left({\dfrac a p}\right)$ is defined as:
 * $\left({\dfrac a p}\right) := a^{\frac{(p - 1)} 2} \pmod p$

Also see

 * Equivalence of Definitions of Legendre Symbol