Václav Šimerka: quadratic forms and factorization

2013/01/01 by Franz Lemmermeyer · 1 citation
Computer Science · Mathematics · #Coding theory and cryptography #Analytic Number Theory Research #Advanced Mathematical Identities

paper · pdf · doi:10.1112/s1461157013000065

openalex publication_date 2013/01/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/31

Abstract

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

Citations

• On Composite Numbers P Which Satisfy the Fermat Congruence a P-1 ≡1 mod P

Cited by

• Carmichael number [wikipedia]

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