On digit sums of multiples of an integer

dc.contributor.authorDartyge, Cécile
dc.contributor.authorLuca, Florian|Stănică, Pantelimon
dc.contributor.departmentApplied Mathematics (MA)
dc.date2009
dc.date.accessioned2020-07-23T19:33:13Z
dc.date.available2020-07-23T19:33:13Z
dc.date.issued2009
dc.descriptionThe article of record as published may be found at https://doi.org/10.1016/j.jnt.2009.04.003
dc.description.abstractLet 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.en_US
dc.description.sponsorshipThe third author was supported by a RIP grant from NPSen_US
dc.format.extent11 p.
dc.identifier.citationDartyge, Cécile, Florian Luca, and Pantelimon Stănică. "On digit sums of multiples of an integer." Journal of Number Theory 129.11 (2009): 2820-2830.
dc.identifier.urihttps://hdl.handle.net/10945/65210
dc.publisherElsevier
dc.rightsThis 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.en_US
dc.subject.authorSum of digitsen_US
dc.subject.authorCarmichael lambda functionen_US
dc.subject.authorSturdy numbersen_US
dc.titleOn digit sums of multiples of an integeren_US
dc.typeArticle
dspace.entity.typePublication
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