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?

I notice that x, y and z are not necessarily distinct.

I understand that Fermat's Last Theorem states that no three positive integers a, b, and c can satisfy the equation aⁿ + bⁿ = cⁿ for any integer value of n greater than two.

My question is, does the same  concept necessarily hold if the indices are not the same?

Posted by brianjn on 2012-05-28 03:14:08