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.

Originally posted by smaia (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.