Modular arithmetic before C. F. Gauss: systematizations and discussions on remainder problems in 18th-century Germany
type: Item
instance of: scholarly article
title: Modular arithmetic before C. F. Gauss: systematizations and discussions on remainder problems in 18th-century Germany
zbMATH Open document ID: 1172.01006
author: Maarten Bullynck
published in: Historia Mathematica
publication date: 2009-03-25T00:00:00Z
review text: Remainder problems have a long tradition and were widely disseminated in books on calculation, algebra, and recreational mathematics. The earliest rules for solving come from ancient China, the general solution method for such problems is today called the Chinese remainder theorem. In Europe many singular solutions for particular cases are known. Bachet de Méziriac showed (1624) how these methods are connected with the Euclidian algorithm and with Diophantic equations. In the 18th-century Germany many scientists and university teacher dealt with the remainder problem, a long list of famous in their time mathematicians is given: Christlieb von Clausberg, C. Wolff, L. Euler, A. Kästner, W. Karsten, L. Lagrange, H. Olbers, C. F. Gauss, J. H. Lambert, C. F. Hindenburg. Clausberg systematized methods that used the greatest common divisor procedure. Euler and Lagrange used fraction solution methods. Hindenburg developed an new system based on finite, combinatorical principles and on direct production of the solution. He formulated the combinatory law of cyclic periods. This was a reach basis for Gauss to construct a general framework from 1791 onwards. The final version appeared in sections I and II of the Disquisitiones Arithmeticae (1801). The new formalism based on Gauss' methods of congruences. The paper is finished by for pages of useful references.
reviewed by: Werner H. Schmidt
Mathematics Subject Classification ID: 01A50
Mathematics Subject Classification ID: 11A05
Mathematics Subject Classification ID: 11D04
zbMATH DE Number: 5532931
zbMATH Keywords: remainder problems
zbMATH Keywords: modular arithmetic
zbMATH Keywords: Euclidean algorithm
zbMATH Keywords: Euler
zbMATH Keywords: Hindenburg
zbMATH Keywords: Gauss
MaRDI profile type: Publication
full work available at URL: j.hm.2008.08.009
OpenAlex ID: W2023508725
Wikidata QID: Q54272008
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DOI: 10.1016/J.HM.2008.08.009
description: scientific article; zbMATH DE number 5532931