IMO Shortlist 2002 problem N6
Dodao/la:
arhiva2. travnja 2012. Find all pairs of positive integers
![m,n\geq3](/media/m/6/b/c/6bc6dbee11fde8aecd8d752adf14f40b.png)
for which there exist infinitely many positive integers
![a](/media/m/6/d/2/6d2832265560bb67cf117009608524f6.png)
such that
![\frac{a^m+a-1}{a^n+a^2-1}](/media/m/8/2/a/82a4b90ca1ca57168c6738690cac402d.png)
is itself an integer.
Laurentiu Panaitopol, Romania
%V0
Find all pairs of positive integers $m,n\geq3$ for which there exist infinitely many positive integers $a$ such that $$\frac{a^m+a-1}{a^n+a^2-1}$$ is itself an integer.
Laurentiu Panaitopol, Romania
Izvor: Međunarodna matematička olimpijada, shortlist 2002