## Number Theory   ## Beal Conjecture Convincing Proof

Authors: A. A. Frempong

The author proves the original Beal conjecture that if A^x + B^y = C^z, where A, B, C, x, y, z are positive integers and x, y, z > 2, then A, B and C have a common prime factor. In the numerical equations, two approaches have been used to change the sum, A^x + B^y, of two powers to a single power, C^z. In one approach, the application of factorization is the main principle, while in the other approach, a formula derived from A^x + B^y was applied. The two approaches changed the sum A^x + B^y to a single power, C^z, perfectly. The derived formula confirmed the validity of the assumption that it is necessary that the sum A^x + B^y has a common prime factor before C^z can be derived. It was concluded that if A^x + B^y = C^z, where A, B, C, x, y, z are positive integers and x, y, z > 2, then A, B and C have a common prime factor.

### Submission history

[v1] 2018-12-25 18:07:31
[v2] 2018-12-28 14:18:23
[v3] 2019-01-01 03:48:04
[v4] 2019-01-01 21:14:39
[v5] 2019-01-04 11:56:04
[v6] 2019-01-05 16:32:17
[v7] 2019-01-08 13:30:23
[v8] 2019-01-15 03:19:29