Originally posted by smaia27^4+162^3=9^7
(or give a counterexample)
If A^x + B^y = C^z where A,B,C,x,y,z are positive integers and x, y, z are all greater than 2, then A, B, and C must have a common prime factor.
This is the Beal conjecture.
http://www.math.unt.edu/~mauldin/beal.html
common prime is 1