IMO Shortlist 2012 problem N6
Dodao/la:
arhiva3. studenoga 2013. Let
![x](/media/m/f/1/8/f185adeed9bd346bc960bca0147d7aae.png)
and
![y](/media/m/c/c/0/cc082a07a517ebbe9b72fd580832a939.png)
be positive integers. If
![x^{2^n}-1](/media/m/5/b/1/5b1b02e81bded5f9a7c4876fd3338053.png)
is divisible by
![2^ny+1](/media/m/b/1/7/b17ecab8bac134819b5fe4548f4dd3d8.png)
for every positive integer
![n](/media/m/a/e/5/ae594d7d1e46f4b979494cf8a815232b.png)
, prove that
![x=1](/media/m/3/4/9/3491fdc1148836187540039de445a211.png)
.
%V0
Let $x$ and $y$ be positive integers. If $x^{2^n}-1$ is divisible by $2^ny+1$ for every positive integer $n$, prove that $x=1$.
Izvor: Međunarodna matematička olimpijada, shortlist 2012