If x, y and z are integers, 3^x+4^y=5^z is satisfied for x=y=z=2.

Are there any other solutions?

x=0, y=1, z=1 is a solution, but one might consider it to be degenerate. Still, the problem didn't forbid any of x,y,z to be zero so I guess it counts.

The question of whether there's another solution with non-zero x,y,z is more interesting, but I don't have an answer for that yet.

Posted by Paul on 2005-09-01 17:15:58