I'd appreciate some hints or advice for this assignment:
Let F be a field of characteristic p and f(x) = x^p - x - c be a polynomial in F[x]. Show that f is either irreducible in F[x] or that all its roots lie in F.
So F=GF(p^n), n>0. If n=1 we have x^p - x - c = x - c, but what properties could I use for general n?