Competition problem — Number theory

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Number theory Difficulty 6.2 National olympiad Prove it

[29.6] Let $a, b$ be positive integers such that $a b+1$ divides $a^{2}+b^{2}$ . Prove: $\left(a^{2}+b^{2}\right) /(a b+1)$ is always a perfect square.

Solution

None

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