(** The other components of ggcd are indeed the correct factors. *)

(* Specifications: *)
Lemma ggcdn_correct_divisors : forall n a b,
let '(g,(aa,bb)) := ggcdn n a b in
a = g*aa /\ b = g*bb.
Lemma ggcd_correct_divisors : forall a b,
let '(g,(aa,bb)) := ggcd a b in
a=g*aa /\ b=g*bb.