Definition R_p4 (x y : Z) :=
  0 <= x /\ 1 < y /\ exists d : Z, y = d * d * x /\ 1 < d.

Lemma prop4b : forall p q : Z, 0 <= p -> 0 <= q -> p <= q -> rel_prime p q -> is_sqr (p * (q * (q * q - p * p))) -> is_sqr p /\ is_sqr q /\ is_sqr (q * q - p * p).