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A functional equation on positive integers with two conditions

Source: Dutch TST 2024, 2.2

June 28, 2024
algebrafunctional equationalgebra proposed

Problem Statement

Find all functions f:Z>0→Z>0f:\mathbb{Z}_{>0} \to \mathbb{Z}_{>0} such that for all positive integers m,nm,n and aa we have a) f(f(m)f(n))=mnf(f(m)f(n))=mn and b) f(2024a+1)=2024a+1f(2024a+1)=2024a+1.
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