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I wonder if the problem I have on my computer with a calculation with WolframAlpha, also occurs on other computers.

The situation is that asking for integer solutions of the equation $$x^2+y^2=5(xy-1)$$ the time delay is much longer than usual and does not end (not that my computer will not function with Wolfram because it responds well to questions others).

This irregularity is not because of the difficulty of the problem since I find without calculator the solutions $(1,3),(2,9),(3,14)$, for example.

Do the same with your computer occur?

Thanks in advance for your comments.

Piquito
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  • On my iPad, WA immediately churns out five pairs of integers, none of which are on your list, and all values are negative! Hmm... – David Quinn May 11 '16 at 22:01
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    Thanks for your answer. (If you pay a little attention you will see that if $(a,b)$ is solution so is $(-a,-b)$). I tried again with my computer and the same: it does not end the computation. I'm intrigued by the case. Thanks again. – Piquito May 11 '16 at 22:11
  • see http://math.stackexchange.com/questions/1780420/characterize-the-integers-a-b-satisfying-ab-1a2b2/1781381#1781381 there are infinitely many solutions. If $(x,y)$ is a solution, so are $(5y-x,y)$ and $(x,5x-y),$ one of which has larger entry sum than what you began with. – Will Jagy May 11 '16 at 23:06
  • @Will Jagy: Surely. The problem here is about the computation with WA. In many other cases where there are infinitely many solutions WA gives quickly several ones, likely what happened with David Quinn above. Thanks you very much. – Piquito May 11 '16 at 23:14

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