\begin{definition}[Definition:Field of Integers Modulo Prime]
Let $p \in \Bbb P$ be a prime number.
Let $\Z_p$ be the set of integers modulo $p$.
Let $+_p$ and $\times_p$ denote addition modulo $p$ and multiplication modulo $p$ respectively.
The algebraic structure $\struct {\Z_p, +_p, \times_p}$ is '''the field of integers modulo $p$'''.
\end{definition}