Question 19
Let $S=\{2,3,4, \ldots\}$ denote the set of integers that are greater than or equal to $2$. Does there exist a function $f: S \rightarrow S$ such that
$$
f(a) f(b) = f\left(a^{2} b^{2}\right) \text{ for all } a, b \in S \text{ with } a \neq b?
$$
$$
f(a) f(b) = f\left(a^{2} b^{2}\right) \text{ for all } a, b \in S \text{ with } a \neq b?
$$