Corollary 3

Tag 05IN, permanent. Cite it as [Bourbaki, Tag 05IN].

Algebra, chapter I, § 9. Fields

Let $a$ be an integer $\geqslant 0$ . For the ring $\mathbf{Z}/a\mathbf{Z}$ to be a field, it is necessary and sufficient that $a$ be prime.

This follows from Corollary 1 and $§ 8$ , no. 11.

For $p$ prime the field $\mathbf{Z}/p\mathbf{Z}$ is denoted by $\mathbf{F}_p$ .

Bourbaki puts the proof directly after the statement, so what is above is the statement and its proof together.

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Nothing.