Given that each of x, y and z is a positive integer, it is observed that the equation 5^x + 12^y = 13^z is satisfied for x=y=z=2.

Does there exist any further solution?

(In reply to Question by brianjn)

Brian, this may interest you:

http://www.ams.org/notices/199711/beal.pdf

Posted by broll on 2012-05-28 11:31:41