by rewrite gcd0p size_polyC oner_eq0.
rewrite ltnS leqn0 size_poly_eq0; move/eqP->; rewrite gcdp0 modp0 size_polyC.
by rewrite oner_eq0.
Qed.

Lemma gcdp_scaler c m n : c != 0 -> gcdp m (c *: n) %= gcdp m n.