IMO Shortlist 1989 problem 10


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2. travnja 2012.
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Let g: \mathbb{C} \rightarrow \mathbb{C}, \omega \in \mathbb{C}, a \in \mathbb{C}, \omega^3 = 1, and \omega \ne 1. Show that there is one and only one function f: \mathbb{C} \rightarrow \mathbb{C} such that
f(z) + f(\omega z + a) = g(z),z\in \mathbb{C}
Izvor: Međunarodna matematička olimpijada, shortlist 1989