On digit sums of multiples of an integer

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Authors
Dartyge, Cécile
Luca, Florian|Stănică, Pantelimon
Subjects
Sum of digits
Carmichael lambda function
Sturdy numbers
Advisors
Date of Issue
2009
Date
2009
Publisher
Elsevier
Language
Abstract
Let g >1 be an integer and sg(m) be the sum of digits in base g of the positive integer m. In this paper, we study the positive integers n such that sg(n) and sg(kn) satisfy certain relations for a fixed, or arbitrary positive integer k. In the first part of the paper, we prove that if n is not a power of g, then there exists a nontrivial multiple of n say kn such that sg (n) = sg (kn). In the second part of the paper, we show that for any K > 0 the set of the integers n satisfying s g (n) K s g (kn) for all k ∈ N is of asymptotic density 0. This gives an affirmative answer to a question of W.M. Schmidt.
Type
Article
Description
The article of record as published may be found at https://doi.org/10.1016/j.jnt.2009.04.003
Series/Report No
Department
Applied Mathematics (MA)
Organization
Identifiers
NPS Report Number
Sponsors
The third author was supported by a RIP grant from NPS
Funder
Format
11 p.
Citation
Dartyge, Cécile, Florian Luca, and Pantelimon Stănică. "On digit sums of multiples of an integer." Journal of Number Theory 129.11 (2009): 2820-2830.
Distribution Statement
Rights
This publication is a work of the U.S. Government as defined in Title 17, United States Code, Section 101. Copyright protection is not available for this work in the United States.
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