**If**A^{x}+ B^{y}= C^{z},**where**A, B, C, x, y, z are all positive integers and x, y, z are all greater than 2,**then**A, B and C must have a common prime factor.

If you can prove the conjecture to be true (or false), you will win a million dollar prize. I can't help you with a proof.

You also win the prize if you can come up with a counterexample. A valid counterexample must have these properties:

- A
^{x}+ B^{y}must equal C^{z} - 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).

If you have a purported counterexample, you can check it here.
Enter values for A, x, B, y, C, z and hit the **Check** button.

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