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$\textbf{Question:}$ Find all positive integers,which are representable uniquely as

$\frac{x^2+y}{xy+1}$

where x and y are positive integers.

I think this question maybe has something to do with vieta jumping. I also found that for such x,y to exist $y < x^2$ must hold.

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    $\begingroup$ See here. Russian Mathematical Olympiad $2001$. $\endgroup$ – Dietrich Burde May 31 at 18:58

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