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...
| Autores: | , |
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| Tipo de recurso: | artículo |
| Estado: | Versión publicada |
| Fecha de publicación: | 2009 |
| País: | Colombia |
| Institución: | Universidad de Antioquia |
| Repositorio: | Repositorio UdeA |
| Idioma: | inglés |
| OAI Identifier: | oai:bibliotecadigital.udea.edu.co:10495/23653 |
| Acceso en línea: | http://hdl.handle.net/10495/23653 |
| Access Level: | acceso abierto |
| Palabra clave: | Teorema de Midy Teoría de los números Numbers, Theory of |
| Sumario: | 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. |
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