IMO Shortlist 2005 problem N4
Dodao/la:
arhiva2. travnja 2012. Find all positive integers
![n](/media/m/a/e/5/ae594d7d1e46f4b979494cf8a815232b.png)
such that there exists a unique integer
![a](/media/m/6/d/2/6d2832265560bb67cf117009608524f6.png)
such that
![0\leq a < n!](/media/m/f/4/7/f47e3a30b7d23c26a2d3b856d718f6e7.png)
with the following property:
%V0
Find all positive integers $n$ such that there exists a unique integer $a$ such that $0\leq a < n!$ with the following property:
$$n!\mid a^n + 1$$
Izvor: Međunarodna matematička olimpijada, shortlist 2005