proposition: Lemma logn_gcd p m n : 0 < m -> 0 < n -> logn p (gcdn m n) = minn (logn p m) (logn p n).
proof: Proof. move=> m_gt0 n_gt0; case p_pr: (prime p); last by rewrite /logn p_pr. by apply: (@expnI p); rewrite ?prime_gt1// expn_min -!p_part partn_gcd. Qed.
imports: mathcomp(ssreflect ssrfun ssrbool eqtype ssrnat seq path) mathcomp(fintype div bigop)