# A Theorem on Repeating Decimals

```@article{Leavitt1967ATO,
title={A Theorem on Repeating Decimals},
author={W. Leavitt},
journal={American Mathematical Monthly},
year={1967},
volume={74},
pages={669-673}
}```
• W. Leavitt
• Published 1 June 1967
• Mathematics
• American Mathematical Monthly
Image Compression Based on Mapping Image Fractals to Rational Numbers
• Computer Science
• IEEE Access
• 2018
A new image compression mechanism that exploits the relationship between rational numbers and their corresponding quotient representation, and shows that a considerable compression ratio can be achieved when the least significant bits of each byte are altered. Expand
Repeating Decimals: A Period Piece
Summary Consider the repeating decimal of a reduced fraction t/n between 0 and 1, where none of the primes 2, 3 or 5 is a factor of n. The fraction satisfies the m-block property if m divides theExpand
On converting discrete logarithm calculation to long division
• Computer Science
• 2016 IEEE International Conference on Recent Trends in Electronics, Information & Communication Technology (RTEICT)
• 2016
The primary goal of this research is to establish the connection between the discrete logarithm and long division. Expand
A SIMPLE PROOF OF MIDY'S THEOREM
• Mathematics
• 2013
In this note we give a method for finding the elements in the period of a periodic rational number. We then use our method to give an elementary proof of Midy’s theorem on repeating decimals. AMSExpand
ON MIDY'S THEOREM IN BASE b
In 1836 E. Midy proved that if the period of a reciprocal of a prime p ≥ 5 has even length and is split into two half-periods, then the sum of the halves is a string of 9's. This result has beenExpand
On Ginsberg Theorem in Base b
In 2004, B. Ginsberg proved that if the period of a reciprocal of a prime p ≥ 5 has length r =3 w and is split into three pieces then their sum is a string of 9’s. In this note we give a very simpleExpand
Artin's Primitive Root Conjecture – A Survey
• P. Moree
• Mathematics, Computer Science
• Integers
• 2012
A survey of the literature on this topic emphasizing the Artin primitive root conjecture (1927) and the contributions in the survey on `elliptic Artin' are due to Alina Cojocaru. Expand
Remainder Wheels and Group Theory
Lawrence Brenton (brenton@math.wayne.edu) was educated at the University of Pennsylvania, the University of Washington in Seattle, and the University of Bonn, Germany. He has served on the faculty ofExpand
Midy's theorem for periodic decimals.
In 1836 E. Midy published at Nantes, France, a pamphlet of twenty-one pages on some topics in number theory with applications to decimals. He was the first to actually prove something about ourExpand
On cyclic numbers and an extension of Midy's theorem
• Mathematics
• 2006
In this note we consider fractions of the form 1/m and their floating-point representation in various arithmetic bases. For instance, what is 1/7 in base 2005? And, what about 1/4? We give a simpleExpand