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FIND ALL f(x) such that (f(m)+n)(f(n)+m) is a perfet square for all m,n natural numbers including 0.
Hi Aritra,
Note that when f(n) = n + λ, where λ is a positive integer, the product becomes
(m+λ+n)(n+λ+m) = (n+m+λ)2, a perfect square.
Now in case if you need a proof (which is indeed quite very challenging, much beyond the difficulty level of IITs), that this is the only function for which, the given expression would be a perfect square, mail me at ashwin.rsmd@gmail.com and i will send you back the proof.
Best Regards,
Ashwin (IIT Madras).
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