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Part of 1984 IMO Shortlist

Problems(1)

Diophantine equations

Source:

9/8/2010
Prove:
(a) There are infinitely many triples of positive integers m,n,pm, n, p such that 4mn−m−n=p2−1.4mn - m- n = p^2 - 1.
(b) There are no positive integers m,n,pm, n, p such that 4mn−m−n=p2.4mn - m- n = p^2.
number theoryDiophantine equationQuadraticpolynomialequationIMO Shortlist