On the decomposition of modular multiplicative inverse operators via a new functional algorithm approach to Bachet’s-Bezout’s Lemma

Luis A. Cortés–Vega

doi:10.1088/1742-6596/936/1/012095

Journal of Physics: Conference Series

Paper • The following article is Open access

On the decomposition of modular multiplicative inverse operators via a new functional algorithm approach to Bachet's-Bezout's Lemma

Luis A. Cortés–Vega¹

Published under licence by IOP Publishing Ltd
Journal of Physics: Conference Series, Volume 936, 6th International Conference on Mathematical Modelling in Physical Sciences (IC-MSQUARE 2017) 28–31 August 2017, Pafos, Cyprus Citation Luis A. Cortés–Vega 2017 J. Phys.: Conf. Ser. 936 012095 DOI 10.1088/1742-6596/936/1/012095

Download Article PDF

Article metrics

440 Total downloads

Article and author information

Author e-mails

luis.cortes@uantof.cl

Author affiliations

¹ Mathematics Department, Antofagasta University, Antofagasta, Chile

Buy this article in print

Journal RSS

Sign up for new issue notifications

Abstract

In this paper, we consider modular multiplicative inverse operators (MMIO)'s of the form:

$\begin{eqnarray}&&{{\mathscr{J}}}_{(m+n)}:{({\mathbb{Z}}/(m+n){\mathbb{Z}})}^{* }\to {\mathbb{Z}}/(m+n){\mathbb{Z}},\text\,{{\mathscr{J}}}_{(m+n)}(a)={a}^{-1}.\end{eqnarray}$

A general method to decompose ${{\mathscr{J}}}_{(m+n)}(.)$ ${{\mathscr{J}}}_{(m+n)}(.)$ over group of units ${({\mathbb{Z}}/(m+n){\mathbb{Z}})}^{* }$ ${({\mathbb{Z}}/(m+n){\mathbb{Z}})}^{* }$ is derived. As result, an interesting decomposition law for these operators over ${({\mathbb{Z}}/(m+n){\mathbb{Z}})}^{* }$ ${({\mathbb{Z}}/(m+n){\mathbb{Z}})}^{* }$ is established. Numerical examples illustring the new results are given. This, complement some recent results obtained by the author for (MMIO)'s defined over group of units of the form ${({\mathbb{Z}}/\varrho {\mathbb{Z}})}^{* }$ ${({\mathbb{Z}}/\varrho {\mathbb{Z}})}^{* }$ with ϱ = m × n > 2.

Export citation and abstract BibTeX RIS

Previous article in issue

Next article in issue

Content from this work may be used under the terms of the Creative Commons Attribution 3.0 licence. Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI.

Please wait… references are loading.

On the decomposition of modular multiplicative inverse operators via a new functional algorithm approach to Bachet's-Bezout's Lemma

Article metrics

Share this article

Author e-mails

Author affiliations

Abstract