[seqfan] Re: Problem from IMO2010

[Jack Brennen]

I'm pretty sure g(k)=k+c is the only class of such functions...

Maybe prove that g(m) and m must have the same periodicities relative to
every prime number p, and then show that g(k)=k+c is the only such
function.




zak seidov wrote:
> Determine all functions g(k) such that
> (g(m)+n)(m+g(n))
> is a perfect square for all positive integers m, n.
>   www.imo2010org.kz
> 
> besides trivial g(k)=k+c (c-integer)
> i don't know other solns :(
> any ideas?
> zak 
> 
> 
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