Divisibility tests and recurring decimals in Euclidean domains
Abstract
In this article, we try to explain and unify standard divisibility tests found in various books. We then look at recurring decimals, and list a few of their properties. We show how to compute the number of digits in the recurring part of any fraction. Most of these results are accompanied by a proof (along with the assumptions needed), that works in a Euclidean domain. We then ask some obvious questions related to the results, and mention some similar questions that have been answered. In the final section (written jointly with P. Moree), some quantitative statements regarding the asymptotic behaviour of various sets of primes satisfying related properties, are considered.
Keywords
Cite
@article{arxiv.math/0406025,
title = {Divisibility tests and recurring decimals in Euclidean domains},
author = {Apoorva Khare},
journal= {arXiv preprint arXiv:math/0406025},
year = {2011}
}
Comments
22 pages, LaTeX, 11pt; to appear in the JP Journal of Algebra, Number Theory, and Applications (JPANTA)