MathDB

National Spain Olympiad 2004, Problem 3

Source: National Spain Olympiad 2004

May 31, 2017

algebraFunctional Equations

Problem Statement

Represent for

\mathbb {Z}

the set of all integers. Find all of the functions

{f:}

\mathbb{Z} \rightarrow \mathbb{Z}

such that for any

{x,y}

integers, they satisfy:

{f(x + f(y)) = f(x) - y.}