IMO Shortlist 1998 problem N5
Dodao/la:
arhiva2. travnja 2012. Determine all positive integers
![n](/media/m/a/e/5/ae594d7d1e46f4b979494cf8a815232b.png)
for which there exists an integer
![m](/media/m/1/3/6/1361d4850444c055a8a322281f279b39.png)
such that
![{2^{n}-1}](/media/m/e/f/7/ef79716045adb84cd03b10110e411bf5.png)
is a divisor of
![{m^{2}+9}](/media/m/a/d/6/ad6e97ad23edde3c825f961527579689.png)
.
%V0
Determine all positive integers $n$ for which there exists an integer $m$ such that ${2^{n}-1}$ is a divisor of ${m^{2}+9}$.
Izvor: Međunarodna matematička olimpijada, shortlist 1998