(** (Order b q p) means the order of b is q in multgroup(Z_p). *)

Definition Order (b : Z) (q p : nat) :=
  0 < q /\
  Mod (Exp b q) 1 p /\ (forall d : nat, 0 < d -> Mod (Exp b d) 1 p -> q <= d).

Lemma order_div : forall (b : Z) (x p : nat), Order b x p -> forall y : nat, 0 < y -> Mod (Exp b y) 1 p -> Divides x y.