Let a function $f$ be defined from $\mathbb{N}$ to $\mathbb{N}$.Let for all natural $m,n$, \[f(m)^{2}+f(n)|(m^{2}+n)^{2}\]
Prove that $f(m)=m$.
F.E.(4)
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Re: F.E.(4)
Please,post the question carefully
- Tahmid Hasan
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Re: F.E.(4)
I think this equation is correct.Furthermore it's an ISL problem.Isn't that right,Sanzeed?shehab ahmed wrote:Please,post the question carefully
বড় ভালবাসি তোমায়,মা
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- Posts:66
- Joined:Tue Mar 20, 2012 12:52 am
Re: F.E.(4)
Oops,sorry.I didn't notice the '|' sign at first sight from my mobile
Re: F.E.(4)
Hmmm. It is really an ISL problem. Just show that $f(1)=1,f(p-1)=p-1$. Then use congruence. That kills the problem.
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Re: F.E.(4)
OOps. Here $p$ is a prime.
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