Is polynomial $f(X)=X^{p^n}-X$ is irreducible and separable in $\mathbb{F_p[X]}$?
I know that derivative of f(X) is $p^{n}X^{p^n-1}-1$ which is 0-1=-1 so it has no multiple root and hence separable; since it is field with $\mathrm{char}=p$ so only question is about irreducibilty?