(** * Relative primality *)
Definition rel_prime (a b:Z) : Prop := Zis_gcd a b 1.
(** Bezout's theorem: [a] and [b] are relatively prime if and only if there exist [u] and [v] such that [ua+vb = 1]. *)

(** Gauss's theorem: if [a] divides [bc] and if [a] and [b] are relatively prime, then [a] divides [c]. *)
Theorem Gauss : forall a b c:Z, (a | b * c) -> rel_prime a b -> (a | c).