proposition: Fact divides_pow p n k : prime p -> p <d n^k -> p <d n.
proof: Proof. intros Hp. induction k as [ | k IHk ]; simpl. + now intros ->%divides_1_inv. + intros []%prime_div_mult; auto. Qed.
imports: List Arith Lia Bool Permutation Undecidability.Shared.Libs.DLW.Utils(utils_tac utils_list utils_nat gcd sums)