Question 43
Find all functions $f: \mathbb{Z}_{\gt 0} \rightarrow \mathbb{Z}_{\gt 0}$ such that for all positive integers $m$, $n$ and $a$ we have
a) $f(f(m) f(n))=m n$,
b) $f(2024 a+1)=2024 a+1$.
a) $f(f(m) f(n))=m n$,
b) $f(2024 a+1)=2024 a+1$.