General Elementary Direct Proof of Fermat's Last Theorem

TL;DR

This paper introduces a new elementary proof of Fermat's Last Theorem using algebra, modular math, and binomial series, establishing a general pattern applicable for all positive integers n.

Contribution

It provides a novel direct elementary proof of Fermat's Last Theorem, expanding the understanding of the theorem with a unified approach for all n.

Findings

Proof confirms Fermat's Last Theorem for all positive integers n

Develops a general pattern applicable to all n

Uses algebra, modular math, and binomial series in the proof

Abstract

This paper presents a novel direct elementary proof for Fermat's Last Theorem. We use algebra, modular math, and binomial series to develop inherent mathematical relationships hidden within Fermat's Last Theorem. With these derived relationships, we are able to develop general pattern applicable for all positive integers of n. Finally, we are able to confirm and complete the direct proof for Fermat's Diophantine equation for all n.