(** ZMod, same as Mod but only uses Z. *)
Definition ZMod (a b n : Z) := exists q : Z, a = (b + n * q)%Z.

Lemma zmoda0_exp_compat :
forall a n : Z,
(n > 0)%Z -> ZMod a 0 n -> forall m : Z, (m > 0)%Z -> ZMod (ZExp a m) 0 n.