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Find all incresing functions

Source: Brazil EGMO TST2 2023 #1

January 29, 2024
increasing functionsstrictly increasingfunctional equationnumber theoryalgebrafunction

Problem Statement

Let Z>0={1,2,3,…}\mathbb{Z}_{>0} = \{1, 2, 3, \ldots \} be the set of all positive integers. Find all strictly increasing functions f:Z>0→Z>0f : \mathbb{Z}_{>0} \rightarrow \mathbb{Z}_{>0} such that f(f(n))=3nf(f(n)) = 3n.
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