Simerka - Quadratic Forms and Factorization

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.