preprint · Preprints.org · 2025
Elementary Proof of Beal’s Conjecture
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Abstract
The 6 variable general equation of Beal’s conjecture equation xa + by = zc, 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 c 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 and expand to all integer solutions of Beal’s equation if they have common prime factor. Second, powers of binomials of coprime integers x, y expand in two terms such that if two of the three terms of the equation are perfect powers the third one is not a perfect power.
Cite this paper
Barghout, K. (2025). Elementary Proof of Beal’s Conjecture. Preprints.org. https://doi.org/10.20944/preprints202501.1436.v1
Barghout, Kamal. “Elementary Proof of Beal’s Conjecture.” Preprints.org, 2025, https://doi.org/10.20944/preprints202501.1436.v1.
Barghout, Kamal. 2025. “Elementary Proof of Beal’s Conjecture.” Preprints.org. https://doi.org/10.20944/preprints202501.1436.v1.
Barghout, K. (2025) ‘Elementary Proof of Beal’s Conjecture’, Preprints.org. Available at: https://doi.org/10.20944/preprints202501.1436.v1.
@misc{barghout2025elementary,
title = {{Elementary Proof of Beal’s Conjecture}},
author = {Barghout, Kamal},
journal = {Preprints.org},
year = {2025},
doi = {10.20944/preprints202501.1436.v1}
}Made from the index record. Check names, capitalisation and page numbers against the paper. Need another style? AI for Research has over 10,000.