Corollary

Tag 06GP, permanent. Cite it as [Bourbaki, Tag 06GP].

Algebra, chapter V, § 1. Prime fields. Characteristic

— Let K be a field and F(X) a polynomial with coefficients in K, whose derivative F'(X) is zero. a) If K is of characteristic 0, then F ∈ K. b) If K is of characteristic p ≠ 0, there exists a polynomial G(X) such that F(X) = G(X^p). For we have dF = F . dX = 0.

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

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