\begin{definition}[Definition:Legendre Symbol/Definition 2]
Let $p$ be an odd prime.
Let $a \in \Z$.
The '''Legendre symbol''' $\left({\dfrac a p}\right)$ is defined as:
:$\left({\dfrac a p}\right) := a^{\frac{(p - 1)} 2} \bmod p$
where $x \bmod y$ denotes the modulo operation.
\end{definition}