This question comes from the 2007 IMO shortlist:
Find all integers $a,b,c$ such that $ab-c$, $bc-a$ and $ca-b$ are powers of two (of the form $2^k$ where $k \geq0$).
What are some methods of finding solutions?
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Leucippus
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Aleksandar
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I impulsively upvoted because the problem is cool, but can you please show us any ideas/working you've come up with/done? Have you looked at similar problems (here on MSE) you can link to that might guide other users in providing an answer? Also, add the tag contest-math if you edit it.Thanks – ShakesBeer Jul 22 '15 at 13:12
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@Shakespeare I don't know where to start to be honest, and yes I have looked for other problems on MSE related to this that might help. – Aleksandar Jul 22 '15 at 13:15
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It is not formally a duplicate, there is no restriction here on positivity of $a,b,c$. For example, a permutations of $(0,-1,-1)$ are also solutions. – A.Γ. Jul 22 '15 at 17:53