Published: 12 April 2024| Version 1 | DOI: 10.17632/7dz6tgnbf9.1
Manouchehr Shaghaghi


Abstract Beal's Conjecture stands as a beacon in the realm of number theory, postulating that for the equation A^x+B^y=C^z, where A, B, C, x, y and z are positive integers and x, y and z are greater than 2, the integers A, B, and C must share a common prime factor. This conjecture, intertwined with Fermat's conjecture, offers a pathway to mathematical elegance and simplicity. Delving into the heart of Beal's Conjecture unveils a captivating narrative of discovery and exploration. At its core, the conjecture not only poses profound implications but also holds within it the seeds of its own validation. The pivotal role played by the largest common integer factor among A, B and C illuminates a path toward unraveling the equation's simplest forms. In academic circles, the discourse surrounding Beal's Conjecture extends beyond its mere formulation. Mathematicians delve into its complexities, seeking to unearth its implications and potential applications. Through meticulous analysis, researchers strive to shed light on the underlying principles governing integer solutions and prime factorization. As the quest to decipher Beal's Conjecture persists, it continues to captivate mathematicians worldwide. Its resolution promises not only to deepen our understanding of fundamental mathematical concepts but also to inspire future avenues of inquiry. In my view, the exploration of Beal's Conjecture serves as a testament to the beauty and complexity inherent in mathematical inquiry. Keywords: Beal's Conjecture, Fermat's Conjecture, number theory, integer solutions, prime factorization, mathematical inquiry



Szechenyi Istvan Egyetem