Residues : The gateway to higher arithmetic I

Por • 1 dic, 2012 • Sección: Educacion

Christian Siebeneicher

Abstract: Residues to a given modulus have been introduced to mathematics by Carl Friedrich Gauss with the definition of congruence in the `Disquisitiones Arithmeticae’. Their extraordinary properties provide the basis for a change of paradigm in arithmetic. By restricting residues to remainders left over by divison Peter Gustav Lejeune Dirichlet – Gauss’s successor in G\»ottingen – eliminated in his `Lectures on number theory’ the fertile concept of residues and attributed with the number-theoretic approach to residues for more than one and a half centuries to obscure Gauss’s paradigm shift in mathematics from elementary to higher arithmetic.

arXiv:1211.6057v1 [math.HO]

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