Given a function $f$ defined on the set of all natural numbers $\mathbb{N}$ with three conditions:
If $m,n$ relatively prime, then $f(mn) = f(m)f(n)$.
$f$ strictly increasing.
$f(2) = 2$.
Find a 4th condition such that the result will be that $f(n)$ must equal $n$ for any natural number $n$. (Of course all the conditions together are needed. Your 4th condition should not make any of these three conditions redundant.)
This is posted in my university website:
[1]: http:// mathstat.uohyd.ernet.in/noticeboard/generaldetails.php?id=12