F.E.(4)

For discussing Olympiad Level Algebra (and Inequality) problems
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SANZEED
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F.E.(4)

Unread post by SANZEED » Fri Jun 08, 2012 12:37 am

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
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Re: F.E.(4)

Unread post by shehab ahmed » Sun Jun 10, 2012 8:29 pm

Please,post the question carefully

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Tahmid Hasan
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Re: F.E.(4)

Unread post by Tahmid Hasan » Sun Jun 10, 2012 8:36 pm

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
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Re: F.E.(4)

Unread post by shehab ahmed » Sun Jun 10, 2012 10:00 pm

Oops,sorry.I didn't notice the '|' sign at first sight from my mobile

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SANZEED
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Re: F.E.(4)

Unread post by SANZEED » Tue Jun 12, 2012 11:00 pm

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

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SANZEED
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Location: Mymensingh, Bangladesh

Re: F.E.(4)

Unread post by SANZEED » Tue Jun 12, 2012 11:02 pm

OOps. :oops: Here $p$ is a prime.
$\color{blue}{\textit{To}} \color{red}{\textit{ problems }} \color{blue}{\textit{I am encountering with-}} \color{green}{\textit{AVADA KEDAVRA!}}$

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