IMO Shortlist 2005 problem N6
Dodao/la:
arhiva2. travnja 2012. Let
![a](/media/m/6/d/2/6d2832265560bb67cf117009608524f6.png)
,
![b](/media/m/e/e/c/eec0d7323095a1f2101fc1a74d069df6.png)
be positive integers such that
![b^n+n](/media/m/5/6/5/565ed18282a7bd3673b502f67b460302.png)
is a multiple of
![a^n+n](/media/m/3/a/3/3a3546820fb4cee735b7f23e9defb430.png)
for all positive integers
![n](/media/m/a/e/5/ae594d7d1e46f4b979494cf8a815232b.png)
. Prove that
![a=b](/media/m/a/9/2/a92b57ffecf4f08b70899188d461ba5f.png)
.
%V0
Let $a$, $b$ be positive integers such that $b^n+n$ is a multiple of $a^n+n$ for all positive integers $n$. Prove that $a=b$.
Izvor: Međunarodna matematička olimpijada, shortlist 2005