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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Autores:
García Pulgarín, Gilberto
Giraldo Salazar, Hernán Alonso
Tipo de recurso:
Article of investigation
Fecha de publicación:
2009
Institución:
Universidad de Antioquia
Repositorio:
Repositorio UdeA
Idioma:
eng
OAI Identifier:
oai:bibliotecadigital.udea.edu.co:10495/23653
Acceso en línea:
http://hdl.handle.net/10495/23653
Palabra clave:
Teorema de Midy
Teoría de los números
Numbers, Theory of
Rights
openAccess
License
http://creativecommons.org/licenses/by/2.5/co/
Description
Summary: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.