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Article Dans Une Revue Historia Mathematica Année : 2009

Modular Arithmetics before C.F. Gauss.

Résumé

emainder problems have a long tradition and were widely disseminated in books on calculation, algebra and recreational mathematics from the 13th century until the 18th century. Many singular solution methods for particular cases were known, but Bachet de Méziriac was the first to see how these methods connected with the Euclidean algorithm and with Diophantine analysis (1624). His general solution method contributed to the theory of equations in France, but went largely unnoticed elsewhere. Later Euler independently rediscovered similar methods, while von Clausberg generalised and systematised methods which used the greatest common divisor procedure. These were followed by Euler's and Lagrange's continued fraction solution methods, and Hindenburg's combinatorial solution. Shortly afterwards, Gauss, in the Disquisitiones Arithmeticae, proposed a new formalism based on his method of congruences and created the modular arithmetic framework in which these problems are posed today.
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Dates et versions

halshs-00663292 , version 1 (26-01-2012)

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  • HAL Id : halshs-00663292 , version 1

Citer

Maarten Bullynck. Modular Arithmetics before C.F. Gauss.: Systematizations and discussions on remainder problems in 18th-century Germany.. Historia Mathematica, 2009, 36 (1), pp.48-72. ⟨halshs-00663292⟩
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