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Václav Šimerka: quadratic forms and factorization

Part of: History of mathematics and mathematicians Computational number theory

Published online by Cambridge University Press:  01 May 2013

F. Lemmermeyer
F. Lemmermeyer*
Affiliation:
Mörikeweg 1,73489 Jagstzell,Germany email [email protected]

Abstract

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In this article we show that the Czech mathematician Václav Šimerka discovered the factorization of $\frac{1}{9} (1{0}^{17} - 1)$ 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.

MSC classification

Secondary: 11Y05: Factorization 01A55: 19th century
Type
Research Article
Information
LMS Journal of Computation and Mathematics , Volume 16 , October 2013 , pp. 118 - 129
Copyright
© The Author(s) 2013 

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