Breaking Boundaries: Discovering the Impossible Counterproof of Beal’s Conjecture

Halima Jibril Mohamed ,Ghedlawit Futzum,Adela Zyfi

doi:10.24297/jam.v17i0.8279

Abstract

This paper will attempt to logically differentiate between two types of fractions and discuss the idea of Zero as a neutral integer. This logic can then be followed to create a counterexample and a proof for Beal’s conjecture.

Highlights

For hundreds of years, mathematicians have been intrigued by the famous conjecture of Pierre Fermat, named Fermat’s Last Theorem
[1] After hundreds of years of effort, Andrew Wiles provided the first proof for this theorem in 1994
[2] Fermat’s Last Theorem has been and continues to be extremely powerful and influential in the field of mathematics, making it possible to prove a large part of the modularity theorem and allowed many other mathematical problems to be solved using new approaches

Summary

Introduction

Mathematicians have been intrigued by the famous conjecture of Pierre Fermat, named Fermat’s Last Theorem. Fermat’s Last Theorem is a number theory conjecture that states: [1]. Where A, B, C, x, y, and z are positive integers with x, y, z > 2, A, B, and C have a common prime factor. This number theory conjecture demonstrates that no solutions in positive integers A, B, C, x, y, z exist, with A, B, and C being pairwise coprime and all of x, y, z being greater than 2. This paper aims to show and demonstrate through examples that a counterproof for the conjecture does exist

Integer: This term will be explained using two different definitions

The name and symbol of Zero

Conclusion

Discussion