(** definition of a "prime number" *)
Definition is_prime (p:nat) := (p<>1)/\(forall (d:nat),(divides p d)->(d=1)\/(d=p)).

Lemma nat_factor : forall (n p:nat),(is_prime p)->(n<>0)->{m:nat | (divides n (power p m))/\~(divides n (power p (m+1)))}.