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IMO Shortlist 2013, Number Theory #6

Source: IMO Shortlist 2013, Number Theory #6

July 10, 2014
functionnumber theoryfunctional equationIMO Shortlist

Problem Statement

Determine all functions f:Q→Zf: \mathbb{Q} \rightarrow \mathbb{Z} satisfying f(f(x)+ab)=f(x+ab) f \left( \frac{f(x)+a} {b}\right) = f \left( \frac{x+a}{b} \right) for all x∈Qx \in \mathbb{Q}, a∈Za \in \mathbb{Z}, and b∈Z>0b \in \mathbb{Z}_{>0}. (Here, Z>0\mathbb{Z}_{>0} denotes the set of positive integers.)
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