Simerka - Quadratic Forms and Factorization
Franz Lemmermeyer

TL;DR
This paper highlights Vaclav Simerka's early discovery of a factorization method using quadratic forms, predating similar algorithms and introducing early examples of Carmichael numbers.
Contribution
It reveals Simerka's pioneering work on quadratic form-based factorization and the first known examples of Carmichael numbers, predating modern algorithms.
Findings
Simerka factored (10^17-1)/9 using quadratic forms
First known examples of Carmichael numbers by Simerka
Simerka's work predates Shanks and Schnorr's algorithms
Abstract
In this article we show that the Czech mathematician Vaclav Simerka discovered the factorization of (10^17-1)/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.
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Taxonomy
TopicsCoding theory and cryptography · Analytic Number Theory Research · Advanced Mathematical Identities
