Characterizations of Midy's Property

ABSTRACT: In 1836 E. Midy published in France an article where he showed that if p is a prime number, such that the smallest repeating sequence of digits in the decimal expansion of 1 p has an even length, when this sequence is broken into two halves of equal length if these parts are added then the...

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Authors: García Pulgarín, Gilberto, Giraldo Salazar, Hernán Alonso
Format: article
Status:Published version
Publication Date:2009
Country:Colombia
Institution:Universidad de Antioquia
Repository:Repositorio UdeA
Language:English
OAI Identifier:oai:bibliotecadigital.udea.edu.co:10495/23653
Online Access:http://hdl.handle.net/10495/23653
Access Level:Open access
Keyword:Teorema de Midy
Teoría de los números
Numbers, Theory of
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spelling Characterizations of Midy's PropertyGarcía Pulgarín, GilbertoGiraldo Salazar, Hernán AlonsoTeorema de MidyTeoría de los númerosNumbers, Theory ofABSTRACT: In 1836 E. Midy published in France an article where he showed that if p is a prime number, such that the smallest repeating sequence of digits in the decimal expansion of 1 p has an even length, when this sequence is broken into two halves of equal length if these parts are added then the result is a string of 9s. Later, J. Lewittes and H. W. Martin generalized this statement when the length of the smallest repeating sequence of digits is e = kd and the sequence is broken into d blocks of equal length and the expansion is over any number base; that fact was named Midy’s property. We will give necessary and sufficient conditions (that are easy to check) for the integer N to satisfy Midy’s property.COL0017217Colgate University, Charles University, and DIMATIAÁlgebra Teoría de Números y Aplicaciones: ERMEstados Unidos2021-10-29T22:33:25Z2021-10-29T22:33:25Z2009info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_2df8fbb1https://purl.org/redcol/resource_type/ARTArtículo de investigación7application/pdfapplication/pdfhttp://hdl.handle.net/10495/236531553-1732engIntegersinfo:eu-repo/semantics/openAccesshttp://creativecommons.org/licenses/by/2.5/co/http://purl.org/coar/access_right/c_abf2https://creativecommons.org/licenses/by/4.0/reponame:Repositorio UdeAinstname:Universidad de Antioquiainstacron:Universidad de Antioquia2021-10-29T22:33:26Z
dc.title.none.fl_str_mv Characterizations of Midy's Property
title Characterizations of Midy's Property
spellingShingle Characterizations of Midy's Property
García Pulgarín, Gilberto
Teorema de Midy
Teoría de los números
Numbers, Theory of
title_short Characterizations of Midy's Property
title_full Characterizations of Midy's Property
title_fullStr Characterizations of Midy's Property
title_full_unstemmed Characterizations of Midy's Property
title_sort Characterizations of Midy's Property
dc.creator.none.fl_str_mv García Pulgarín, Gilberto
Giraldo Salazar, Hernán Alonso
author García Pulgarín, Gilberto
author_facet García Pulgarín, Gilberto
Giraldo Salazar, Hernán Alonso
author_role author
author2 Giraldo Salazar, Hernán Alonso
author2_role author
dc.subject.none.fl_str_mv Teorema de Midy
Teoría de los números
Numbers, Theory of
topic Teorema de Midy
Teoría de los números
Numbers, Theory of
description ABSTRACT: In 1836 E. Midy published in France an article where he showed that if p is a prime number, such that the smallest repeating sequence of digits in the decimal expansion of 1 p has an even length, when this sequence is broken into two halves of equal length if these parts are added then the result is a string of 9s. Later, J. Lewittes and H. W. Martin generalized this statement when the length of the smallest repeating sequence of digits is e = kd and the sequence is broken into d blocks of equal length and the expansion is over any number base; that fact was named Midy’s property. We will give necessary and sufficient conditions (that are easy to check) for the integer N to satisfy Midy’s property.
publishDate 2009
dc.date.none.fl_str_mv 2009
2021-10-29T22:33:25Z
2021-10-29T22:33:25Z
dc.type.none.fl_str_mv info:eu-repo/semantics/article
info:eu-repo/semantics/publishedVersion
http://purl.org/coar/resource_type/c_2df8fbb1
https://purl.org/redcol/resource_type/ART
Artículo de investigación
format article
status_str publishedVersion
dc.identifier.none.fl_str_mv http://hdl.handle.net/10495/23653
1553-1732
url http://hdl.handle.net/10495/23653
identifier_str_mv 1553-1732
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv Integers
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
http://creativecommons.org/licenses/by/2.5/co/
http://purl.org/coar/access_right/c_abf2
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eu_rights_str_mv openAccess
rights_invalid_str_mv http://creativecommons.org/licenses/by/2.5/co/
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dc.format.none.fl_str_mv 7
application/pdf
application/pdf
dc.publisher.none.fl_str_mv Colgate University, Charles University, and DIMATIA
Álgebra Teoría de Números y Aplicaciones: ERM
Estados Unidos
publisher.none.fl_str_mv Colgate University, Charles University, and DIMATIA
Álgebra Teoría de Números y Aplicaciones: ERM
Estados Unidos
dc.source.none.fl_str_mv reponame:Repositorio UdeA
instname:Universidad de Antioquia
instacron:Universidad de Antioquia
instname_str Universidad de Antioquia
instacron_str Universidad de Antioquia
institution Universidad de Antioquia
reponame_str Repositorio UdeA
collection Repositorio UdeA
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