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 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.

• 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/