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If $a,b,q=\frac{a^2+b^2}{ab+1}$ are positive integers then $q$ is a perfect square.

Ross Millikan
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Mayank jha
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  • Hey this is an inmo question – AAkash Mar 04 '15 at 18:08
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    Let $a=2$ and $b=3$, then $\frac{13}7$ is not perfect square. –  Mar 04 '15 at 18:10
  • @rubik, your edit isn't same as original question. –  Mar 04 '15 at 18:11
  • 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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    possible duplicate of [Alternative proof that $(a^2+b^2)/(ab+1)$ is a square when it's an integer](http://math.stackexchange.com/questions/28438/alternative-proof-that-a2b2-ab1-is-a-square-when-its-an-integer) Also a link [here](http://math.stackexchange.com/questions/94069/fraca2b21ab-is-a-perfect-square-whenever-it-is-an-integer) – Ross Millikan Mar 04 '15 at 18:14
  • @Mathematician171 You're right, I'm sorry. Thanks for noticing. – rubik Mar 04 '15 at 18:20

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