MathDB

IMO Shortlist 2011, Number Theory 3

Source: IMO Shortlist 2011, Number Theory 3

July 11, 2012

functionalgebranumber theoryDivisibilityIMO ShortlistHi

Problem Statement

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