• THE BEAL CONJECTURE

Abstract

The field of Algebra and Number Theory has a vast number of applications. The Beal Conjecture has been pondered and written by the Texas billionaire Andrew Beal. It started when he became interested in solving the 350-year old mystery of Fermat's Last Theorem. Andrew Wiles proved this theorem in 1994 that, for all n-positive integers, there are no solutions. For example, if n = 3, Wiles proved that there were no solutions. Now since we have n = 3, what if all three exponents were different integers higher from two, then will the integers a, b, and c have the same prime factor? Conversely, if the integers a, b, and c have the same prime factor, would the integer exponents be higher than two?