JP Journal of Algebra, Number Theory and Applications
Volume 7, Issue 1, Pages 1 - 32
(February 2007)
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DIVISIBILITY TESTS AND RECURRING DECIMALS IN EUCLIDEAN DOMAINS
Apoorva Khare (U. S. A.)
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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 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 and phrases: divisibility tests, recurring decimal expansion |
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