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)

 Posts: 66
 Joined: Tue Mar 20, 2012 12:52 am
Re: F.E.(4)
Please,post the question carefully
 Tahmid Hasan
 Posts: 665
 Joined: Thu Dec 09, 2010 5:34 pm
 Location: Khulna,Bangladesh.
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

 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 $f(1)=1,f(p1)=p1$. Then use congruence. That kills the problem.
$\color{blue}{\textit{To}} \color{red}{\textit{ problems }} \color{blue}{\textit{I am encountering with}} \color{green}{\textit{AVADA KEDAVRA!}}$
Re: F.E.(4)
OOps. Here $p$ is a prime.
$\color{blue}{\textit{To}} \color{red}{\textit{ problems }} \color{blue}{\textit{I am encountering with}} \color{green}{\textit{AVADA KEDAVRA!}}$