A note on Pascal's triangle and division by eleven

Bibliographic Details
Main Author: Carvalho, Leonardo Ribeiro de Castro
Publication Date: 2022
Other Authors: Capelas de Oliveira, Edmundo
Format: Article
Language: eng
Source: Revista Intermaths
Download full: https://periodicos2.uesb.br/intermaths/article/view/11094
Summary: Divisibility is an old topic that to this day intrigues and fascinates researchers and scholars. Several rules are well-known in particular the divisibility by eleven, since, for example, a palindrome with an even number of digits is divisible by eleven. In current times, divisibility has its applications, for example, in cryptography. Here, in this paper, we will show that applying two somewhat intuitive procedures to the lines of Pascal's triangle shall always yield numbers divisible by eleven. Illustrative examples are presented.
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spelling A note on Pascal's triangle and division by elevenUma nota sobre o triângulo de Pascal e a divisão por onzePascal's triangleDivisibilityPalindromesStifel's relationshipBinomial theoremTriângulo de PascalDivisibilidadePalíndromosRelação de StifelTeorema do binômioDivisibility is an old topic that to this day intrigues and fascinates researchers and scholars. Several rules are well-known in particular the divisibility by eleven, since, for example, a palindrome with an even number of digits is divisible by eleven. In current times, divisibility has its applications, for example, in cryptography. Here, in this paper, we will show that applying two somewhat intuitive procedures to the lines of Pascal's triangle shall always yield numbers divisible by eleven. Illustrative examples are presented.Universidade Estadual do Sudoeste da Bahia2022-12-31info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionArtigo avaliado pelos Paresapplication/pdfhttps://periodicos2.uesb.br/intermaths/article/view/1109410.22481/intermaths.v3i2.11094INTERMATHS; v. 3 n. 2 (2022); 29-37INTERMATHS; Vol. 3 Núm. 2 (2022); 29-37INTERMATHS; Vol. 3 No. 2 (2022); 29-372675-8318reponame:Revista Intermathsinstname:Universidade Estadual do Sudoeste da Bahia (UESB)instacron:UESBenghttps://periodicos2.uesb.br/intermaths/article/view/11094/7287Copyright (c) 2022 INTERMATHSinfo:eu-repo/semantics/openAccessCarvalho, Leonardo Ribeiro de CastroCapelas de Oliveira, Edmundo2025-05-03T18:04:36Zoai:ojs.pkp.sfu.ca:article/11094Revistahttps://periodicos2.uesb.br/index.php/intermaths/indexPUBhttps://periodicos2.uesb.br/index.php/intermaths/oaiintermaths@uesb.edu.br || publicacoes.digitais@uesb.edu.br2675-83182675-8318opendoar:2025-05-03T18:04:36Revista Intermaths - Universidade Estadual do Sudoeste da Bahia (UESB)false
dc.title.none.fl_str_mv A note on Pascal's triangle and division by eleven
Uma nota sobre o triângulo de Pascal e a divisão por onze
title A note on Pascal's triangle and division by eleven
spellingShingle A note on Pascal's triangle and division by eleven
Carvalho, Leonardo Ribeiro de Castro
Pascal's triangle
Divisibility
Palindromes
Stifel's relationship
Binomial theorem
Triângulo de Pascal
Divisibilidade
Palíndromos
Relação de Stifel
Teorema do binômio
title_short A note on Pascal's triangle and division by eleven
title_full A note on Pascal's triangle and division by eleven
title_fullStr A note on Pascal's triangle and division by eleven
title_full_unstemmed A note on Pascal's triangle and division by eleven
title_sort A note on Pascal's triangle and division by eleven
author Carvalho, Leonardo Ribeiro de Castro
author_facet Carvalho, Leonardo Ribeiro de Castro
Capelas de Oliveira, Edmundo
author_role author
author2 Capelas de Oliveira, Edmundo
author2_role author
dc.contributor.author.fl_str_mv Carvalho, Leonardo Ribeiro de Castro
Capelas de Oliveira, Edmundo
dc.subject.por.fl_str_mv Pascal's triangle
Divisibility
Palindromes
Stifel's relationship
Binomial theorem
Triângulo de Pascal
Divisibilidade
Palíndromos
Relação de Stifel
Teorema do binômio
topic Pascal's triangle
Divisibility
Palindromes
Stifel's relationship
Binomial theorem
Triângulo de Pascal
Divisibilidade
Palíndromos
Relação de Stifel
Teorema do binômio
description Divisibility is an old topic that to this day intrigues and fascinates researchers and scholars. Several rules are well-known in particular the divisibility by eleven, since, for example, a palindrome with an even number of digits is divisible by eleven. In current times, divisibility has its applications, for example, in cryptography. Here, in this paper, we will show that applying two somewhat intuitive procedures to the lines of Pascal's triangle shall always yield numbers divisible by eleven. Illustrative examples are presented.
publishDate 2022
dc.date.none.fl_str_mv 2022-12-31
dc.type.driver.fl_str_mv info:eu-repo/semantics/article
info:eu-repo/semantics/publishedVersion
Artigo avaliado pelos Pares
format article
status_str publishedVersion
dc.identifier.uri.fl_str_mv https://periodicos2.uesb.br/intermaths/article/view/11094
10.22481/intermaths.v3i2.11094
url https://periodicos2.uesb.br/intermaths/article/view/11094
identifier_str_mv 10.22481/intermaths.v3i2.11094
dc.language.iso.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv https://periodicos2.uesb.br/intermaths/article/view/11094/7287
dc.rights.driver.fl_str_mv Copyright (c) 2022 INTERMATHS
info:eu-repo/semantics/openAccess
rights_invalid_str_mv Copyright (c) 2022 INTERMATHS
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
dc.publisher.none.fl_str_mv Universidade Estadual do Sudoeste da Bahia
publisher.none.fl_str_mv Universidade Estadual do Sudoeste da Bahia
dc.source.none.fl_str_mv INTERMATHS; v. 3 n. 2 (2022); 29-37
INTERMATHS; Vol. 3 Núm. 2 (2022); 29-37
INTERMATHS; Vol. 3 No. 2 (2022); 29-37
2675-8318
reponame:Revista Intermaths
instname:Universidade Estadual do Sudoeste da Bahia (UESB)
instacron:UESB
instname_str Universidade Estadual do Sudoeste da Bahia (UESB)
instacron_str UESB
institution UESB
reponame_str Revista Intermaths
collection Revista Intermaths
repository.name.fl_str_mv Revista Intermaths - Universidade Estadual do Sudoeste da Bahia (UESB)
repository.mail.fl_str_mv intermaths@uesb.edu.br || publicacoes.digitais@uesb.edu.br
_version_ 1840460155762769920

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