proposition: Lemma powX_eq_mod i j : i = j %[mod #|qT|.-1] -> 'qX ^+ i = 'qX ^+ j :> qT.
proof: Proof. set n := _.-1 => iEj. rewrite [i](divn_eq i n) [j](divn_eq j n) !exprD ![(_ * n)%N]mulnC. by rewrite !exprM !qX_order_card !expr1n !mul1r iEj. Qed.
imports: HB(structures) mathcomp(ssreflect ssrfun ssrbool eqtype ssrnat seq choice fintype tuple) mathcomp(div bigop binomial finset finfun ssralg countalg finalg) mathcomp(poly polydiv qpoly perm fingroup falgebra fieldext finfield galois) mathcomp(finalg zmodp matrix vector)