Artículos con la etiqueta ‘Aritmética’

Models of true arithmetic are integer parts of nice real closed fields

Por • 7 ago, 2013 • Category: Educacion

Exploring further the connection between exponentiation on real closed fields and the existence of an integer part modelling strong fragments of arithmetic, we demonstrate that each model of true arithmetic is an integer part of an exponential real closed field that is elementary equivalent to the reals with exponentiation.
arXiv:1307.6595v1 [math.LO]

Residues : The gateway to higher arithmetic I

Por • 1 dic, 2012 • Category: Educacion

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.

The Arithmetic of Carmichael Quotients

Por • 21 ago, 2011 • Category: Educacion

Carmichael quotients for an integer $m\ge 2$ are introduced analogous to Fermat quotients, by using Carmichael function $\lambda(m)$. Various properties of these new quotients are investigated, with special emphasis on congruences. Besides, Carmichael-Wieferich numbers are defined and numerous properties are considered.

Dismal Arithmetic

Por • 10 jul, 2011 • Category: Ciencia y tecnología

Dismal arithmetic is just like the arithmetic you learned in school, only simpler: there are no carries, when you add digits you just take the largest, and when you multiply digits you take the smallest. This paper studies basic number theory in this world, including analogues of the primes, number of divisors, sum of divisors, and the partition function.