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f(m + f(n)) = n + f(m + 95)

Source: IMO Shortlist 1995, S6

August 10, 2008
functionalgebrafunctional equationIMO Shortlist

Problem Statement

Let N \mathbb{N} denote the set of all positive integers. Prove that there exists a unique function f:N↦N f: \mathbb{N} \mapsto \mathbb{N} satisfying f(m \plus{} f(n)) \equal{} n \plus{} f(m \plus{} 95) for all m m and n n in N. \mathbb{N}. What is the value of \sum^{19}_{k \equal{} 1} f(k)?
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