IMO Shortlist 1995 problem S6


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2. travnja 2012.
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Let \mathbb{N} denote the set of all positive integers. Prove that there exists a unique function f: \mathbb{N} \mapsto \mathbb{N} satisfying
f(m + f(n)) = n + f(m + 95)
for all m and n in \mathbb{N}. What is the value of \sum^{19}_{k = 1} f(k)?
Izvor: Međunarodna matematička olimpijada, shortlist 1995