Prove:
(a) There are infinitely many triples of positive integers

such that

(b) There are no positive integers

such that
%V0
Prove:
(a) There are infinitely many triples of positive integers $m, n, p$ such that $4mn - m- n = p^2 - 1.$
(b) There are no positive integers $m, n, p$ such that $4mn - m- n = p^2.$