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Characterizations of Midy's Property
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Gilberto García-Pulgarín
Veröffentlicht/Copyright:
15. Juni 2009
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 
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 9′s. 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.
Received: 2008-05-30
Accepted: 2009-03-04
Published Online: 2009-06-15
Published in Print: 2009-June
© de Gruyter 2009
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Artikel in diesem Heft
- Symmetric Numerical Semigroups Generated by Fibonacci and Lucas Triples
- On Newman's Conjecture and Prime Trees
- The Dying Rabbit Problem Revisited
- A Note on the q-Binomial Rational Root Theorem
- The 3x + 1 Conjugacy Map over a Sturmian Word
- The Number of Relatively Prime Subsets of {1, 2, . . . , n}
- Generalized Levinson–Durbin Sequences and Binomial Coefficients
- Neither (4k2 + 1) nor (2k(k – 1) + 1) is a Perfect Square
- Some Arithmetic Properties of Overpartition k-Tuples
- Characterizations of Midy's Property
Artikel in diesem Heft
- Symmetric Numerical Semigroups Generated by Fibonacci and Lucas Triples
- On Newman's Conjecture and Prime Trees
- The Dying Rabbit Problem Revisited
- A Note on the q-Binomial Rational Root Theorem
- The 3x + 1 Conjugacy Map over a Sturmian Word
- The Number of Relatively Prime Subsets of {1, 2, . . . , n}
- Generalized Levinson–Durbin Sequences and Binomial Coefficients
- Neither (4k2 + 1) nor (2k(k – 1) + 1) is a Perfect Square
- Some Arithmetic Properties of Overpartition k-Tuples
- Characterizations of Midy's Property
