IMO Shortlist 2013 problem N6


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21. rujna 2014.
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Determine the functions f : \mathbb{Q} \to \mathbb{Z} satisfying 
  f \left( \frac{f(x) + a}{b} \right ) = f \left( \frac{x + a}{b} \right )
for all x \in \mathbb{Q}, a \in \mathbb{Z}, and b \in \mathbb{Z}_{>0}. (Here, \mathbb{Z}_{>0} denotes the set of positive integers.)
Izvor: Israel