Let $k$ be a finite field. Then there exist a prime number $p$ and an integer $n \in \mathbb{N}$ such that
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\begin{align*}
|k| = p^n.
\end{align*}
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More precisely, $p = \operatorname{char}(k)$, the prime subfield of $k$ is isomorphic to $\mathbb{F}_p$, and, through this prime subfield identification, $k$ is a finite-dimensional [vector space](/page/Vector%20Space) over $\mathbb{F}_p$ of dimension $n$.