ILL 1984 Problem 13

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 $4mn - m- n = p^2.$

Dataset text AoPS wiki problems. Quoted with source.

Solutions

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