IMO 1989 LL GBR26

Let a, b, c, d be positive integers such that ab = cd and a + b =

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IMO 1989 LL GBR26

Origin: GBR

Problem

Let a, b, c, d be positive integers such that ab = cd and a + b = c −d. Prove that there exists a right-angled triangle the measures of whose sides (in some unit) are integers and whose area measure is ab square units.