Problem

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

Tags: functional, functional equation, algebra



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