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Archive for October, 2008

11. PEN K11 (Canada 2002) Find all functions f: \mathbb{N}_{0}\to \mathbb{N}_{0} such that for all

m, \, n\in \mathbb{N}_{0}:

mf(n)+nf(m)=(m+n)f(m^{2}+n^{2}).

Here, \mathbb{N}_{0} denote the set of all nonnegative integers.

Here is the official solution file: pen11.pdf.
You can also discuss the problems here!

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Hi everyone. PEN is BACK. Here goes the first problem of the second season!

11. PEN K11 (Canada 2002) Find all functions f: \mathbb{N}_{0}\to \mathbb{N}_{0} such that for all
m, \, n\in \mathbb{N}_{0}:

mf(n)+nf(m)=(m+n)f(m^{2}+n^{2}).

Here, \mathbb{N}_{0} denote the set of all nonnegative integers.

This problem is suggested by Alexander Remorov from Canada. Next week, his solution will be posted!

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