Question 2
Let $S=\{2,3,4,\ldots\}$. Does there exist a function $f:S\to S$ such that
$$f(a)f(b)=f(a^2b^2)\quad\text{for all distinct }a,b\in S?$$
Proposed by Angelo Di Pasquale, Australia.
$$f(a)f(b)=f(a^2b^2)\quad\text{for all distinct }a,b\in S?$$
Proposed by Angelo Di Pasquale, Australia.