IMO Shortlist 2013 problem A5


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21. rujna 2014.
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Let \mathbb{Z}_{\geq0} be the set of all nonnegative integers. Find all the functions f : \mathbb{Z}_{\geq0} \to \mathbb{Z}_{\geq0} satisfying the relation 
  f(f(f(n))) = f(n + 1) + 1
for all n \in \mathbb{Z}_{\geq0}.
Izvor: Serbia