A new characterization of prime numbers and solution to Lehmer's conjecture on Euler's totient function

TL;DR

This paper uses elementary symmetric polynomials and number theory to solve Lehmer's conjecture on Euler's totient function and introduces a new way to characterize prime numbers.

Contribution

It provides a novel characterization of prime numbers and resolves Lehmer's conjecture using elementary symmetric polynomials and number theory techniques.

Findings

Lehmer's conjecture on Euler's totient function is solved.

A new characterization of prime numbers is established.

The approach combines elementary symmetric polynomials with number theory results.

Abstract

By using the elementary symmetric polynomials and some results of number theory, we solve the well known problem of Lehmer on Euler's totient function. As application, we obtain a new characterization of prime numbers.