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(* 02110-1301 USA                                                     *)
(** Relative primality *)
Definition rel_prime (a b : Z) : Prop := 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)%Z -> rel_prime a b -> (a | c)%Z.