Competition problem — Number theory

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Number theory Difficulty 5.3 AIME, harder Prove it Belarus

Four positive integers $x$ , $y$ , $z$ and $t$ satisfy the relations
$xy - zt = x + y = z + t.$
Is it possible that both $xy$ and $zt$ are perfect squares?

Solution

2. See IMO-2018 Shortlist, Problem N5.

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Source: MathNet, licensed CC-BY-4.0. Statement reproduced verbatim; metadata (topic, difficulty) added by this project.