Keywords
n-residual set
n-adic residuals
n-graphs
raíces primitivas
conjunto n-residual
residuos n-ádicos
n-grafos
How to Cite
Abstract
In this study we analyze the behavior of the residuals of a module, raised to a power n and its relation with the n-residual sets, the graphs of residuals of power, called n-residual graphs and the primitive roots in the same module. With the obtained sets, the reduced graphs and complementary trees were established some properties that are analyzed in routines developed with Mathematica, providing a visual interpretation of the structures, object of the study, and allowing several tests with different values for odd prime number p. With obtained some interesting conjectures with possible formal results.
References
D. M. Burton, Elementary Number Theory, revised printing, Allyn and Bacon Inc, Estados Unidos, 1980.
R. D. Carmichael, The Theory of Numbers, John Wiley & Sons Inc, New York, 1914.
C. F. Gauss, Disquisitiones Arithmeticae, traducción en español, Universidad de Costa Rica, Costa Rica, 1995.
F. Lemmermeyer, Introduction to Number Theory, manuscript, 2000.
F. Lemmermeyer, Reciprocity Laws: From Euler to Eisenstein, Springer- Verlag, Berlín Heidelberg, 2000.
W. J. Leveque, Teoría Elemental de los Números, Centro Regional de Ayuda Técnica, México, 1968.
Math Pages. Number theory, https://www.mathpages.com/home/inumber.htm
I, Niven, H. Zuckerman, Introducción a la Teoría de Números, Editorial Limusa, México, 1969.
F. A. Toranzos, Introducción a la Teoría de Grafos, Secretaría General de la OEA, Washington, DC, 1976.
I. Vinográdov, Fundamentos de la Teoría de los Números, 2nd ed., Editorial Mir, Moscú, 1977.
D. R. Wilkins, Course 311: Michaelmas term 2005, part I: topics in number theory, David R. Wilkins, 1997-2005.
Comments
This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License.
Copyright (c) 2019 Revista de Matemática: Teoría y Aplicaciones