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

Lemma relp_pq1 : forall p q : Z, p >= 0 -> p <= q -> (rel_prime p q) -> (distinct_parity p q) -> (rel_prime (q * q - p * p) (p * p + q * q)).