IMO Shortlist 2011 problem A4


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23. lipnja 2013.
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Determine all pairs (f,g) of functions from the set of positive integers to itself that satisfy

f^{g(n)+1}(n) + g^{f(n)}(n) = f(n+1) - g(n+1) + 1

for every positive integer n. Here, f^k(n) means \underbrace{f(f(\ldots f)}_{k}(n) \ldots )).

Proposed by Bojan Bašić, Serbia
Izvor: Međunarodna matematička olimpijada, shortlist 2011