\begin{definition}[Definition:Quadratic Residue/Character]
Let $p$ be an odd prime.
Let $a \in \Z$ be an integer such that $a \not \equiv 0 \pmod p$.
$a$ is either a quadratic residue or a quadratic non-residue of $p$.
Whether it is or not is known as the '''quadratic character of $a$ modulo $p$'''.
\end{definition}