MathDB

Functional equation

Source: IMO Shortlist 1989, Problem 10, ILL 29

December 26, 2005

functionalgebrafunctional equationcomplex numbersIMO Shortlist

Problem Statement

Let

g: \mathbb{C} \rightarrow \mathbb{C}

\omega \in \mathbb{C}

a \in \mathbb{C}

, \omega^3 \equal{} 1, and

\omega \ne 1

. Show that there is one and only one function

f: \mathbb{C} \rightarrow \mathbb{C}

such that f(z) \plus{} f(\omega z \plus{} a) \equal{} g(z),z\in \mathbb{C}