Every arithmetic progression contains infinitely many \(b\)-Niven numbers

Every arithmetic progression contains infinitely many \(b\)-Niven numbers

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.

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Veröffentlicht in:arXiv.org 2023-03
Hauptverfasser: Harrington, Joshua, Litman, Matthew, Wong, Tony W H
Format: Artikel
Sprache:eng
Schlagworte:
Arithmetic
Integers
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Zusammenfassung: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.
ISSN:2331-8422
DOI:10.48550/arxiv.2303.06534