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ADDITIVE BASES AND NIVEN NUMBERS

Part of: Elementary number theory Sequences and sets

Published online by Cambridge University Press:  25 March 2021

CARLO SANNA Open the ORCID record for CARLO SANNA [Opens in a new window]
CARLO SANNA*
Affiliation:
Department of Mathematical Sciences, Politecnico di Torino, Corso Duca degli Abruzzi 24, 10129 Torino, Italy
*
e-mail: carlo.sanna.dev@gmail.com
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Abstract

Let $g \geq 2$ be an integer. A natural number is said to be a base-g Niven number if it is divisible by the sum of its base-g digits. Assuming Hooley’s Riemann hypothesis, we prove that the set of base-g Niven numbers is an additive basis, that is, there exists a positive integer $C_g$ such that every natural number is the sum of at most $C_g$ base-g Niven numbers.

Keywords

additive basisdigitsNiven numbersum of digits

MSC classification

Primary: 11B13: Additive bases, including sumsets
Secondary: 11A63: Radix representation; digital problems

Information

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 104 , Issue 3 , December 2021 , pp. 373 - 380
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Copyright
© 2021 Australian Mathematical Publishing Association Inc.

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Footnotes

C. Sanna is a member of GNSAGA of INdAM and of CrypTO, the group of Cryptography and Number Theory of Politecnico di Torino.

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