If $a,b,q=\frac{a^2+b^2}{ab+1}$ are positive integers then $q$ is a perfect square.
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Hey this is an inmo question – AAkash Mar 04 '15 at 18:08
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1Let $a=2$ and $b=3$, then $\frac{13}7$ is not perfect square. – Mar 04 '15 at 18:10
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@rubik, your edit isn't same as original question. – Mar 04 '15 at 18:11
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The solution there. http://artofproblemsolving.com/community/c3046h1056472_one_binary_form For the case which you said. – individ Mar 04 '15 at 18:11
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1possible duplicate of Alternative proof that $(a^2+b^2)/(ab+1)$ is a square when it's an integer Also a link here – Ross Millikan Mar 04 '15 at 18:14
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@Mathematician171 You're right, I'm sorry. Thanks for noticing. – rubik Mar 04 '15 at 18:20