Definition R_fact (x y : Z) :=
1 < x /\ 1 < y /\ exists q : Z, y = q * x /\ 1 < q.

Lemma Zfact : forall a : Z, 1 < a -> exists b : Z, (b | a) /\ prime b.
Definition R_p4 (x y : Z) :=
0 <= x /\ 1 < y /\ exists d : Z, y = d * d * x /\ 1 < d.