On a particular case of the Dirichlet's theorem and the Midy's property

TL;DR

This paper provides new characterizations of Midy's property and uses these insights to offer a novel proof of a specific case of Dirichlet's theorem on primes in arithmetic progressions.

Contribution

It introduces new characterizations of Midy's property and applies them to give a fresh proof of a special case of Dirichlet's theorem.

Findings

New characterizations of Midy's property

A novel proof of a special case of Dirichlet's theorem

Enhanced understanding of primes in arithmetic progressions

Abstract

We give new characterizations of the Midy's property and using these results we obtain a new proof of a special case of the Dirichlet's theorem about primes in arithmetic progression.