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Does there exist a pair of strictly monotonic funct

Source: Hungary-Israel Binational Olympiad 2009, Problem 3

August 17, 2009

functioninductioninequalitiesalgebra unsolvedalgebra

Problem Statement

Does there exist a pair

(f; g)

of strictly monotonic functions, both from

\mathbb{N}

\mathbb{N}

, such that

f(g(g(n))) < g(f(n))

for every

n \in\mathbb{N}