Download PDFOpen PDF in browserA Note on the Beal ConjectureEasyChair Preprint no. 13819, version 47 pages•Date: July 6, 2024AbstractAround $1637$, 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 wellknown 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
