Number Theory

    

The Generalised Fermat Equation Pa^x + Qb^y=rc^z and Related Problems

Authors: Julian Beauchamp

The focus of this paper is the generalised Fermat equation, Pa^x + Qb^y=Rc^z, considered by Henri Darmon and Andrew Granville. It is closely related to a family of theorems and conjectures including the Fermat-Catalan Conjecture, the Darmon-Granville Theorem, the Beal Conjecture (also known as the Tijdeman-Zagier Conjecture) and Fermat's Last Theorem. We will consider these briefly before offering a proof that no solutions exist even for P,Q,R>1, for cases x,y,z>2, using a new binomial identity for a^x + b^y to an indeterminate power, z. The proof extends to its corollaries the Beal Conjecture and Fermat's Last Theorem.

Comments: 6 Pages.

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Submission history

[v1] 2021-03-18 20:52:09
[v2] 2021-03-23 19:26:49 (removed)
[v3] 2021-03-25 15:48:10

Unique-IP document downloads: 340 times

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