IMO 1998 - Shortlisted Problems Question 13

(BUL) IMO6. Determine the least possible value of $f(1998)$, where $f$ is a function from the set $\mathbb N$ of positive integers into itself such that for all $m,n\in\mathbb N$,
$$f(n^2f(m))=m[f(n)]^2.$$