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EVERY ARITHMETIC PROGRESSION CONTAINS INFINITELY MANY b-NIVEN NUMBERS

Part of: Elementary number theory Sequences and sets

Published online by Cambridge University Press:  31 July 2023

JOSHUA HARRINGTON Open the ORCID record for JOSHUA HARRINGTON [Opens in a new window] ,
MATTHEW LITMAN Open the ORCID record for MATTHEW LITMAN [Opens in a new window]  and
TONY W. H. WONG Open the ORCID record for TONY W. H. WONG [Opens in a new window]
JOSHUA HARRINGTON
Affiliation:
Department of Mathematics, Cedar Crest College, 100 College Dr, Allentown, PA 18104, USA e-mail: joshua.harrington@cedarcrest.edu
MATTHEW LITMAN
Affiliation:
Department of Mathematics, University of California, Davis, 1 Shields Ave, Davis, CA 95616, USA e-mail: mclitman@ucdavis.edu
TONY W. H. WONG*
Affiliation:
Department of Mathematics, Kutztown University of Pennsylvania, 15200 Kutztown Rd, Kutztown, PA 19530, USA
*
e-mail: wong@kutztown.edu
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Abstract

For an integer $b\geq 2$, a positive integer is called a b-Niven number if it is a multiple of the sum of the digits in its base-b representation. In this article, we show that every arithmetic progression contains infinitely many b-Niven numbers.

Keywords

Niven numberarithmetic progression

MSC classification

Primary: 11A63: Radix representation; digital problems
Secondary: 11B25: Arithmetic progressions

Information

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 109 , Issue 3 , June 2024 , pp. 409 - 413
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Copyright
© The Author(s), 2023. Published by Cambridge University Press on behalf of Australian Mathematical Publishing Association Inc.

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References

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