## Proof of Beal’s Conjecture and Related Examples

**Authors:** Kamal Barghout

In this article we prove Beal’s conjecture by deductive reasoning by means of elementary algebraic methods. The main assertion in the proof stands upon that the LHS of Beal’s equation represents the sum of two single-term polynomial functions with common indeterminate x of value greater than 1. The single term polynomial function on the RHS of Beal’s equation can be built from the sum of the two polynomials on the LHS. The Greatest Common Factor (GCF) of the two terms on the LHS of the equation is a number in exponential form whose base is the common indeterminate of the two polynomials. Upon factorization of the GCF, it must be combined with the sum of the two coefficients of the terms to yield the single-term polynomial on the RHS of the equation.

**Comments:** 16 Pages. The material in this article is copyrighted. Please obtain authorization to use from the author

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### Submission history

[v1] 2017-12-05 15:21:45

[v2] 2017-12-07 09:57:31

[v3] 2017-12-09 13:15:45

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