Show that if $x, y, z$ are positive integers, then $(xy + 1)(yz + 1)(zx + 1)$ is a perfect square if and only if $xy + 1, yz + 1, zx+1$ are perfect squares.
$(xy + 1)(yz + 1)(zx + 1) $ is a perfect square if and only if each factor is
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number-theory
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7Intriguing but not informative title... – 2011-12-17
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12googling (xy + 1)(yz + 1)(zx + 1) gives http://www.jstor.org/stable/2691347 – 2011-12-17
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1@sdcvvc, maybe you can summarize the contents of that paper here so that the question doesn't remain unanswered. – 2011-12-18