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Old function problem (IMO SL 1987-P22)

Source:

August 19, 2010
functionalgebrafunctional equationIMO ShortlistIMOIMO 1987

Problem Statement

Does there exist a function f:Nā†’Nf : \mathbb N \to \mathbb N, such that f(f(n))=n+1987f(f(n)) =n + 1987 for every natural number nn? (IMO Problem 4)
Proposed by Vietnam.
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