Let $f$ be a function taking the positive integers to the positive integers, such that
\[f(mf(n)) = nf(m)\]for all positive integers $m$ and $n.$  Find the smallest possible value of $f(2007).$
Question:
Let $f$ be a function taking the positive integers to the positive integers, such that
\[f(mf(n)) = nf(m)\]for all positive integers $m$ and $n.$  Find the smallest possible value of $f(2007).$
Answer:
Let's think step by step.

user
18
Let $f$ be a function taking the positive integers to the positive integers, such that
\[f(mf(n)) = nf(m)\]for all positive integers $m$ and $n.$  Find the smallest possible value of $f(2007).$
train