(* Complements about power and number theory. *)

(* Specifications: *)
Lemma Zpower_divide p q : 0 < q -> (p | p ^ q).
Theorem rel_prime_Zpower_r i p q :
0 <= i -> rel_prime p q -> rel_prime p (q^i).
Theorem rel_prime_Zpower i j p q :
0 <= i ->  0 <= j -> rel_prime p q -> rel_prime (p^i) (q^j).
Theorem prime_power_prime p q n :
0 <= n -> prime p -> prime q -> (p | q^n) -> p = q.
Theorem Zdivide_power_2 x p n :
0 <= n -> 0 <= x -> prime p -> (x | p^n) -> exists m, x = p^m.