split;split;[split | intros | split | intros];try (apply one_min_div);elim H0;intros;elim H;intros;apply H4;split;trivial;elim H2;intro q;intro;rewrite H5;[exists (q*c) | exists (q*b)];ring.
Qed.

(** if gcd(a,d)=1 then gcd(a,d^n)=1 *)
Lemma rel_prime_power : forall (d a n:nat),(rel_prime a d)->(rel_prime a (power d n)).
induction n;simpl;intros.