IMO Shortlist 2000 problem N2
Dodao/la:
arhiva2. travnja 2012. For every positive integers
![n](/media/m/a/e/5/ae594d7d1e46f4b979494cf8a815232b.png)
let
![d(n)](/media/m/8/b/5/8b5ba2b86903af1640ec9f08b90773b6.png)
the number of all positive integers of
![n](/media/m/a/e/5/ae594d7d1e46f4b979494cf8a815232b.png)
. Determine all positive integers
![n](/media/m/a/e/5/ae594d7d1e46f4b979494cf8a815232b.png)
with the property:
![d^3(n) = 4n](/media/m/7/9/c/79cb03cf6213ffb640c8f35372ac680e.png)
.
%V0
For every positive integers $n$ let $d(n)$ the number of all positive integers of $n$. Determine all positive integers $n$ with the property: $d^3(n) = 4n$.
Izvor: Međunarodna matematička olimpijada, shortlist 2000