In one of the proof in the book "Abstract Algebra'' by Dummit and Foote (Theorem 41, pg. 554) we have a monic polynomial $g(x)\in\mathbb{Z}[x]$, and the book claims that $g(x^{p})=(g(x))^{p}\mod p$
Can someone please explain why this is true ? I know that $\forall a\in\mathbb{F}_{p}:a=a^{p}$, but I don't see how this imply the equality as polynomials