IMO Shortlist 2000 problem N3
Dodao/la:
arhiva2. travnja 2012. Does there exist a positive integer
![n](/media/m/a/e/5/ae594d7d1e46f4b979494cf8a815232b.png)
such that
![n](/media/m/a/e/5/ae594d7d1e46f4b979494cf8a815232b.png)
has exactly 2000 prime divisors and
![n](/media/m/a/e/5/ae594d7d1e46f4b979494cf8a815232b.png)
divides
![2^n + 1](/media/m/a/f/c/afca65342225c5da6784045b53448477.png)
?
%V0
Does there exist a positive integer $n$ such that $n$ has exactly 2000 prime divisors and $n$ divides $2^n + 1$?
Izvor: Međunarodna matematička olimpijada, shortlist 2000