intros.
elim H;intro q;intro.
elim H0;intro q';intro.
exists (q+q').
rewrite H1;rewrite H2.
ring.
Qed.

(** if d | a then d | a*b *)
Lemma divides_mult : forall (d a b:nat),(divides a d)->(divides (a*b) d).
unfold divides.