\begin{definition}[Definition:Biquadratic Residue]
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 '''biquadratic residue of $p$''' {{iff}} $x^4 \equiv a \pmod p$ has a solution.
That is, {{iff}}:
: $\exists x \in \Z: x^4 \equiv a \pmod p$
\end{definition}