IMO Shortlist 2011 problem N3
Dodao/la:
arhiva23. lipnja 2013. Let
![n \geq 1](/media/m/a/9/8/a982fcac3e2c9e0d94e965d6efb5a582.png)
be an odd integer. Determine all functions
![f](/media/m/9/9/8/99891073047c7d6941fc8c6a39a75cf2.png)
from the set of integers to itself, such that for all integers
![x](/media/m/f/1/8/f185adeed9bd346bc960bca0147d7aae.png)
and
![y](/media/m/c/c/0/cc082a07a517ebbe9b72fd580832a939.png)
the difference
![f(x)-f(y)](/media/m/2/4/f/24f46cc551684c43734e054c1ace5b4b.png)
divides
![x^n-y^n.](/media/m/3/3/d/33dd51e7a20ec55b4ce2ce519ec8fabf.png)
Proposed by Mihai Baluna, Romania
%V0
Let $n \geq 1$ be an odd integer. Determine all functions $f$ from the set of integers to itself, such that for all integers $x$ and $y$ the difference $f(x)-f(y)$ divides $x^n-y^n.$
Proposed by Mihai Baluna, Romania
Izvor: Međunarodna matematička olimpijada, shortlist 2011