Simerka - Quadratic Forms and Factorization

2011/12/31 by Franz Lemmermeyer, Lemmermeyer, Franz
Computer Science · Mathematics · #01A55 #11A51 #Advanced Mathematical Identities #Analytic Number Theory Research #Coding theory and cryptography #FOS: Mathematics #History and Overview (math.HO) #Number Theory (math.NT) #math.HO #math.NT #msc:01A55 #msc:11A51

paper · pdf · doi:10.48550/arxiv.1201.0282

arxiv created 2011/12/31 · openalex publication_date 2011/12/31 · arxiv updated 2012/01/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this article we show that the Czech mathematician Vaclav Simerka discovered the factorization of (10¹7-1)/9 using a method based on the class group of binary quadratic forms more than 120 years before Shanks and Schnorr developed similar algorithms. Simerka also gave the first examples of what later became known as Carmichael numbers.

Related

• Václav Šimerka: quadratic forms and factorization
• Deducing factoring methods through concrete material
• Binary quadratic forms: modern developments
• Binary quadratic forms and the factorization method of Gauss
• The Carmichael numbers up to 10¹⁸