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f(f(m)f(n)) = mn, f(2022a + 1) = 2022a + 1

Source: Switzerland - 2022 Swiss Final Round p3

November 17, 2022
algebrafunctional equationfunctional

Problem Statement

Let NN be the set of positive integers. Find all functions f:N→Nf : N \to N such that both ∙\bullet f(f(m)f(n))=mnf(f(m)f(n)) = mn ∙\bullet f(2022a+1)=2022a+1f(2022a + 1) = 2022a + 1 hold for all positive integers m,nm, n and aa.
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