By computerized searching, greatly accelerated by aid of modular arithmetic, this conjecture has been verified for all values of all six variables up to 1000.[2] So in any counterexample, at least one of the variables must be greater than 1000.
A variation of the conjecture where x, y, z (instead of A, B, C) must have a common prime factor is not true. See, for example 274 + 1623 = 97.
Beal's conjecture is a generalization of Fermat's last theorem, which corresponds to the case x = y = z. If ax + bx = cx with , then either the bases are coprime or share a common factor. If they share a common factor, it can be divided out of each to yield an equation with smaller, coprime bases.
The conjecture is not valid over the larger domain of Gaussian integers. After a prize of $50 was offered for a counterexample, Fred W. Helenius provided (−2 + i)3 + (−2 − i)3 = (1 + i)4.[3
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http://en.wikipedia.org/wiki/Beals%5Fconjecturei did not read what i pasted in here i just know how to google things.