IMO Shortlist 1998 problem N6
Dodao/la:
arhiva2. travnja 2012. For any positive integer
![n](/media/m/a/e/5/ae594d7d1e46f4b979494cf8a815232b.png)
, let
![\tau (n)](/media/m/5/a/9/5a9dce5a57ccfbc46529cb23bf9ed016.png)
denote the number of its positive divisors (including 1 and itself). Determine all positive integers
![m](/media/m/1/3/6/1361d4850444c055a8a322281f279b39.png)
for which there exists a positive integer
![n](/media/m/a/e/5/ae594d7d1e46f4b979494cf8a815232b.png)
such that
![\frac{\tau (n^{2})}{\tau (n)}=m](/media/m/9/f/3/9f32634596d1e59739ecac0865305825.png)
.
%V0
For any positive integer $n$, let $\tau (n)$ denote the number of its positive divisors (including 1 and itself). Determine all positive integers $m$ for which there exists a positive integer $n$ such that $\frac{\tau (n^{2})}{\tau (n)}=m$.
Izvor: Međunarodna matematička olimpijada, shortlist 1998