(a) Let p be a prime and assume either (i) char K = p or (ii) char K ≠ p and K contains a primitive pth root of unity. Then x^P - a ϵ K[x] is either irreducible or splits in K[x].

(b) If char K = p ≠ 0, then for any root u of x^P - a ϵ K[x], K(u) ≠ K(u^P) if and only if f K(u) : K] = p.