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f(n)f(m)=f ((nm)^{2021})

Source: 2021 3nd Final Mathematical Cup Senior Division P1 FMC

October 30, 2022
functionalfunctional equationalgebra

Problem Statement

Let NN is the set of all positive integers. Determine all mappings f:N−{1}→Nf: N-\{1\} \to N such that for every n≠mn \ne m the following equation is true f(n)f(m)=f((nm)2021)f(n)f(m)=f\left((nm)^{2021}\right)
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