## F.E.(4)

For discussing Olympiad Level Algebra (and Inequality) problems
SANZEED
Posts: 550
Joined: Wed Dec 28, 2011 6:45 pm

### F.E.(4)

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 $f(m)=m$.
$\color{blue}{\textit{To}} \color{red}{\textit{ problems }} \color{blue}{\textit{I am encountering with-}} \color{green}{\textit{AVADA KEDAVRA!}}$

shehab ahmed
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

### Re: F.E.(4)

shehab ahmed wrote:Please,post the question carefully
I think this equation is correct.Furthermore it's an ISL problem.Isn't that right,Sanzeed?
বড় ভালবাসি তোমায়,মা

shehab ahmed
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

SANZEED
Posts: 550
Joined: Wed Dec 28, 2011 6:45 pm

### 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.
$\color{blue}{\textit{To}} \color{red}{\textit{ problems }} \color{blue}{\textit{I am encountering with-}} \color{green}{\textit{AVADA KEDAVRA!}}$

SANZEED
Posts: 550
Joined: Wed Dec 28, 2011 6:45 pm
OOps. Here $p$ is a prime.
$\color{blue}{\textit{To}} \color{red}{\textit{ problems }} \color{blue}{\textit{I am encountering with-}} \color{green}{\textit{AVADA KEDAVRA!}}$