IMO Shortlist 1989 problem 27
Dodao/la:
arhiva2. travnja 2012. Let
![m](/media/m/1/3/6/1361d4850444c055a8a322281f279b39.png)
be a positive odd integer,
![m > 2.](/media/m/8/2/c/82c8509fb6bf72b77866d4c8f77cda01.png)
Find the smallest positive integer
![n](/media/m/a/e/5/ae594d7d1e46f4b979494cf8a815232b.png)
such that
![2^{1989}](/media/m/c/5/1/c51d966dda4855c456cbd4ef4f0c4338.png)
divides
%V0
Let $m$ be a positive odd integer, $m > 2.$ Find the smallest positive integer $n$ such that $2^{1989}$ divides $m^n - 1.$
Izvor: Međunarodna matematička olimpijada, shortlist 1989