Powers of p in bases of the form 2p
DOI:
https://doi.org/10.35819/remat2023v9i2id6625Keywords:
Recurrence Relation, Powers, Even Numerical BasesAbstract
In this work, we will explore the calculation of powers of p in bases of the form 2p. We will see that if p is even and n>=2, then the power p^n (in base 2p) has the unit digit equal to 0. In the case in which p is odd of the form p=2q+1, with q even, the power p^n (in base 2p) has the unit digit equal to p and the second-order digit equal to q. Furthermore, we will see that such powers can be recursively obtained by through a division by 2 and the addition of specific digits to the right of this quotient.
Downloads
References
COSTA, E. A.; SANTOS, R. Números de Ball Generalizados. Revista Sergipana de Matemática e Educação Matemática, v. 7, n. 1, p. 61-85, 2022. DOI: https://doi.org/10.34179/revisem.v7i1.16202.
COXFORD A. F.; SHULTE, A. P. The Ideas of Algebra, K-12. Yearbook, Reston, VA: NCTM, 1988.
FOMÍN, S. V. Sistemas de Numeración. Moscou: MIR-Moscou, 1975.
HEFEZ, A. Aritmética. Coleção PROFMAT. 2. ed. Rio de Janeiro: SBM, 2016.
KUMAYAMA, H. Algoritmo da multiplicação em uma linha. Revista do Professor de Matemática, Rio de Janeiro, n. 22, 1991. Disponível em: https://rpm.org.br/cdrpm/22/3.htm. Acesso em: 10 maio 2023.
MACHADO, P. A. M. A Lei de Alcides. Revista do Professor de Matemática, Rio de Janeiro, n. 37, 1998. Disponível em: https://rpm.org.br/cdrpm/37/1rpm.htm. Acesso em: 11 maio 2023.
MILIES, C. F. P. M.; COELHO, S. P. Números: Uma Introdução à Matemática. 3. ed. São Paulo: Editora da USP, 2006.
ROCHA, K. F. Bases numéricas não usuais: um breve estudo. Orientador: Rogério de Oliveira. 2019. 88 f. Dissertação (Mestrado em Matemática) - Universidade Federal da Grande Dourados, Dourados, MS, 2019.
Downloads
Published
How to Cite
Issue
Section
License
Copyright (c) 2023 REMAT: Revista Eletrônica da Matemática
This work is licensed under a Creative Commons Attribution 4.0 International License.
REMAT retains the copyright of published articles, having the right to first publication of the work, mention of first publication in the journal in other published media and distribution of parts or of the work as a whole in order to promote the magazine.
This is an open access journal, which means that all content is available free of charge, at no cost to the user or his institution. Users are permitted to read, download, copy, distribute, print, search or link the full texts of the articles, or use them for any other legal purpose, without requesting prior permission from the magazine or the author. This statement is in accordance with the BOAI definition of open access.
