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A Note on the Beal Conjecture

EasyChair Preprint 13819, version 3

Versions: 1234history
7 pagesDate: July 5, 2024

Abstract

Around $1637$, Pierre de Fermat famously scribbled, and claimed to have a proof for, his statement that equation $a^{n} + b^{n} = c^{n}$ has no positive integer solutions for exponents $n>2$. The theorem stood unproven for centuries until Andrew Wiles' groundbreaking work in $1994$, with a notable caveat: Wiles' proof, while successful, relied on modern tools far beyond Fermat's claimed approach in terms of complexity. Combining short and basic tools, we were able to prove the Beal conjecture, a well-known generalization of Fermat's Last Theorem. The present work potentially offers a solution which is closer in spirit to Fermat's original idea.

Keyphrases: Binomial theorem, Fermat's Equation, Linear Diophantine Equations, prime numbers

BibTeX entry
BibTeX does not have the right entry for preprints. This is a hack for producing the correct reference:
@booklet{EasyChair:13819,
  author    = {Frank Vega},
  title     = {A Note on the Beal Conjecture},
  howpublished = {EasyChair Preprint 13819},
  year      = {EasyChair, 2024}}
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