If char K = p ≠ 0, let K_p= {u^p - u| u ϵ K}.

(a) A cyclic extension field F of K of degree p exists if and only if K ≠ K_P.

(b) If there exists a cyclic extension of degree p of K, then there exists a cyclic extension of degree p^n-1 for every n ≥ 1.