Number Theory

    

Proof of Beal’s Conjecture

Authors: Kamal Barghout

The 6 variable general equation of Beal’s conjecture equation〖 x〗^a+y^b=z^c, where x, y, z, a, b, and c are positive integers, and a,b,c≥3, is identified as an identity made by expansion of powers of binomials of integers x and y; where x, y and z have common prime factor. Here, a proof of the conjecture is presented in two folds. First, powers of binomials of integers x and y expand to all integer solutions of Beal’s equation if they have common prime factor. Second, powers of binomials of coprime positive integers x and y expand to two terms such that if one of them is a perfect power the other one is not a perfect power.

Comments: 4 Pages.

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Submission history

[v1] 2025-01-07 22:05:08

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