Section UnityRoots.
Variable n : nat.
(* Showing the existence of a primitive root requires the theory in cyclic. *)
Variable z : F.
Hypothesis prim_z : n.-primitive_root z.
Let zn := [seq z ^+ i | i <- index_iota 0 n].

Lemma factor_Xn_sub_1 : \prod_(0 <= i < n) ('X - (z ^+ i)%:P) = 'X^n - 1.