IMO Shortlist 2007 problem N1
Dodao/la:
arhiva2. travnja 2012. Find all pairs of natural numbers
![(a, b)](/media/m/0/5/9/059101434c13a86d8297575c7ee676ea.png)
such that
![7^a - 3^b](/media/m/b/0/2/b02e2293d1970b4d2b2ab1521da3526c.png)
divides
![a^4 + b^2](/media/m/6/6/1/6612b5766474fc020e7666e0de0971ad.png)
.
Author: Stephan Wagner, Austria
%V0
Find all pairs of natural numbers $(a, b)$ such that $7^a - 3^b$ divides $a^4 + b^2$.
Author: Stephan Wagner, Austria
Izvor: Međunarodna matematička olimpijada, shortlist 2007