Number Theory

    

Empirical and Theoretical Validation of Beal's Conjecture

Authors: Óscar Reguera García

Beal's Conjecture posits that for any solution to the equation A^x + B^y = C^z with A, B, C beingpositive integers without common prime factors and x, y, z being integers greater than 2, A, B, and C must share at least one common prime factor. This study conducts a comprehensive empirical andtheoretical validation of the conjecture, using a combined theoretical analysis with computationalsimulations. No counterexamples were found in the extended range of 2 to 10,000 for A, B, C, and 3to 10 for x, y, z.

Comments: 8 Pages.

Download: PDF

Submission history

[v1] 2024-07-02 20:18:39

Unique-IP document downloads: 372 times

Vixra.org is a pre-print repository rather than a journal. Articles hosted may not yet have been verified by peer-review and should be treated as preliminary. In particular, anything that appears to include financial or legal advice or proposed medical treatments should be treated with due caution. Vixra.org will not be responsible for any consequences of actions that result from any form of use of any documents on this website.

Add your own feedback and questions here:
You are equally welcome to be positive or negative about any paper but please be polite. If you are being critical you must mention at least one specific error, otherwise your comment will be deleted as unhelpful.

comments powered by Disqus