Necessary condition for divisibility by the power of prime ideal and its application to Fermat's Last Theorem

TL;DR

The paper establishes a necessary divisibility condition for integral elements related to prime ideals and applies this to provide a straightforward proof of Fermat's Last Theorem.

Contribution

It introduces a new necessary condition for divisibility by prime powers and applies it to simplify the proof of Fermat's Last Theorem.

Findings

Established a necessary condition for divisibility by prime powers.

Provided a simplified proof of Fermat's Last Theorem.

Linked prime ideal divisibility to classical number theory results.

Abstract

In the paper one proves a necessary condition for divisibility of integral elements by the powers of prime divisor of unramifed prime ideal and gives its application to a simple proof of Fermat's Last Theorem.