IMO Shortlist 2003 problem N6
Dodao/la:
arhiva2. travnja 2012. Let
![p](/media/m/1/c/8/1c85c88d10b11745150467bf9935f7de.png)
be a prime number. Prove that there exists a prime number
![q](/media/m/c/1/d/c1db9b1124cc69b01f9a33595637de69.png)
such that for every integer
![n](/media/m/a/e/5/ae594d7d1e46f4b979494cf8a815232b.png)
, the number
![n^p-p](/media/m/5/3/4/534003c7aa9760153aed857bf4d3643a.png)
is not divisible by
![q](/media/m/c/1/d/c1db9b1124cc69b01f9a33595637de69.png)
.
%V0
Let $p$ be a prime number. Prove that there exists a prime number $q$ such that for every integer $n$, the number $n^p-p$ is not divisible by $q$.
Izvor: Međunarodna matematička olimpijada, shortlist 2003