Determine the least possible value of where is a function from the set of positive integers into itself such that for all ,
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Determine the least possible value of $f(1998),$ where $f$ is a function from the set ${\bf N}$ of positive integers into itself such that for all $m,n\in {\bf N}$,
$$f\left( n^{2}f(m)\right) =m\left[ f(n)\right] ^{2}.$$
Izvor: Međunarodna matematička olimpijada, shortlist 1998
Školjka 
where 
is a function from the set 
of positive integers into itself such that for all 
, ![f\left( n^{2}f(m)\right) =m\left[ f(n)\right] ^{2}.](/media/m/d/0/d/d0d1f5a0ff4ad4cf2a895d94af1a10b4.png)