A Note on the Beal Conjecture

EasyChair Preprint 13819, version 4

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

@booklet{EasyChair:13819,
  author    = {Frank Vega},
  title     = {A Note on the Beal Conjecture},
  howpublished = {EasyChair Preprint 13819},
  year      = {EasyChair, 2024}}