If you can prove the conjecture to be true (or false), you will win a million dollar prize.
One way to prove it false is to come up with a counterexample.
A valid counterexample must have these properties:
Ax + By must equal Cz
A, B, C, x, y, z must all be positive integers
x, y, z must all be greater than 2
A, B, C must have no common factor (other than 1).
Check your counterexample here:
Enter values for A, x, B, y, C, z and hit the Check button.