Algebraic proofs of Fermats last theorem and Beals conjecture

James E Joseph

doi:10.24297/jam.v12i9.132

Abstract

In this paper, the following statememt of Fermats Last Theorem is proved. If x, y, z are positive integersï° is an odd prime and z = x y , x, y, z ï° ï° ï° ï€« are all even. Also, in this paper, is proved (Beals conjecture) The equationï¸ ï ï® z = x ï€« y has no solution in relatively prime positive integers x, y, z, with ï¸ ,ï,ï® primes at least .

Highlights

The equation z = x y has no solution in relatively prime positive integers x, y, z, with, primes at least 3 has not been given an algebraic solution
For other theorems named after Pierre de Fermat, see [1]
The case = 2 was known to have infinitely many solutions. This theorem was first conjectured by Pierre de Fermat in 1637 in the margin of a copy of Arithmetica where he claimed he had a proof that was too large to fit in the margin

Summary

Introduction

For other theorems named after Pierre de Fermat, see [1]. Fermat’s Last Theorem (sometimes called Fermat’s conjecture, especially in older texts) states that no three positive integers x, y, and z satisfy the equation z = x y for any integer value of greater than two. This theorem was first conjectured by Pierre de Fermat in 1637 in the margin of a copy of Arithmetica where he claimed he had a proof that was too large to fit in the margin.

Results

Conclusion