# 2001 IMO Shortlist Problems/A1

Revision as of 22:12, 17 July 2009 by Brut3Forc3 (talk | contribs)

## Problem

Let denote the set of all ordered triples of nonnegative integers. Find all functions such that

## Solution

We can see that for and for satisfies the equation. Suppose there exists another solution . Let . Plugging in we see that satisfies the relationship , so that each value of is equal to 6 points around it with an equal sum . This implies that for fixed , is constant. Furthermore, some values of are always zero; for example, by the problem statement, and similarly, , so . Thus, must be identically zero, so is the only function satisfying this equation.