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f (n + f (n)) = 1, f (1998) = 2 (Chile NMO 1999 P7)

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November 27, 2021
algebrafunctional equationfunctional

Problem Statement

Let ff be a function defined on the set of positive integers , and with values in the same set, which satisfies: ∙\bullet f(n+f(n))=1f (n + f (n)) = 1 for all n≥1n\ge 1. ∙\bullet f(1998)=2f (1998) = 2 Find the lowest possible value of the sum f(1)+f(2)+...+f(1999)f (1) + f (2) +... + f (1999), and find the formula of ff for which this minimum is satisfied,
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