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

2012/03/06 by John H. Castillo, Castillo, John H., Gilberto García-Pulgarín +3
Mathematics · #11A05 #11A07 #11A15 #11A63 #16U60 #Analytic Number Theory Research #FOS: Mathematics #Finite Group Theory Research #Limits and Structures in Graph Theory #Number Theory (math.NT) #math.NT #msc:11A05 #msc:11A07 #msc:11A15 #msc:11A63 #msc:16U60

paper · pdf · doi:10.48550/arxiv.1203.1273

6 pages

arxiv created 2012/03/06 · openalex publication_date 2012/03/06 · arxiv updated 2012/03/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Citations

• Midy's Theorem for Periodic Decimals
• The primes contain arbitrarily long arithmetic progressions

Cited by

• Pseudoprimes stronger than strong pseudoprimes

Related

• Formalization of the prime number theorem and Dirichlet's theorem
• An alternative proof of the Dirichlet prime number theorem
• Dirichlet's Theorem and Jacobsthal's Function
• On a Special Case of Dirichlet's Theorem
• The concept of "character" in Dirichlet's theorem on primes in an arithmetic progression