IMO Shortlist 2006 problem N7
Dodao/la:
arhiva2. travnja 2012. For all positive integers
![n](/media/m/a/e/5/ae594d7d1e46f4b979494cf8a815232b.png)
, show that there exists a positive integer
![m](/media/m/1/3/6/1361d4850444c055a8a322281f279b39.png)
such that
![n](/media/m/a/e/5/ae594d7d1e46f4b979494cf8a815232b.png)
divides
![2^{m} + m](/media/m/5/b/0/5b0f418988c8e1308249cb274bfef92d.png)
.
%V0
For all positive integers $n$, show that there exists a positive integer $m$ such that $n$ divides $2^{m} + m$.
Izvor: Međunarodna matematička olimpijada, shortlist 2006