On the distribution in residue classes of integers with a fixed sum of digits

Christian Mauduit, Carl Pomerance, A. Sárközy

Research output: Contribution to journalArticle

16 Citations (Scopus)

Abstract

We give an asymptotic formula for the distribution of those integers n in a residue class, such that n has a fixed sum of base-g digits, with some uniformity over the choice of the modulus and g. We then use this formula to solve the problem of I. Niven of giving an asymptotic formula for the distribution of those integers n divisible by the sum of their base-g digits. Our results also allow us to give a stronger form of a result of M. Olivier dealing with the distribution of integers with a given gcd with their sum of base-g digits.

Original languageEnglish
Pages (from-to)45-62
Number of pages18
JournalRamanujan Journal
Volume9
Issue number1-2
DOIs
Publication statusPublished - Mar 2005

Fingerprint

Digit
Asymptotic Formula
Integer
Divisible
Uniformity
Modulus
Class

Keywords

  • Niven numbers
  • Sum-of-digits function

ASJC Scopus subject areas

  • Algebra and Number Theory

Cite this

On the distribution in residue classes of integers with a fixed sum of digits. / Mauduit, Christian; Pomerance, Carl; Sárközy, A.

In: Ramanujan Journal, Vol. 9, No. 1-2, 03.2005, p. 45-62.

Research output: Contribution to journalArticle

Mauduit, Christian ; Pomerance, Carl ; Sárközy, A. / On the distribution in residue classes of integers with a fixed sum of digits. In: Ramanujan Journal. 2005 ; Vol. 9, No. 1-2. pp. 45-62.
@article{8b318d83df29413086b1e3659102e080,
title = "On the distribution in residue classes of integers with a fixed sum of digits",
abstract = "We give an asymptotic formula for the distribution of those integers n in a residue class, such that n has a fixed sum of base-g digits, with some uniformity over the choice of the modulus and g. We then use this formula to solve the problem of I. Niven of giving an asymptotic formula for the distribution of those integers n divisible by the sum of their base-g digits. Our results also allow us to give a stronger form of a result of M. Olivier dealing with the distribution of integers with a given gcd with their sum of base-g digits.",
keywords = "Niven numbers, Sum-of-digits function",
author = "Christian Mauduit and Carl Pomerance and A. S{\'a}rk{\"o}zy",
year = "2005",
month = "3",
doi = "10.1007/s11139-005-0824-6",
language = "English",
volume = "9",
pages = "45--62",
journal = "Ramanujan Journal",
issn = "1382-4090",
publisher = "Springer Netherlands",
number = "1-2",

}

TY - JOUR

T1 - On the distribution in residue classes of integers with a fixed sum of digits

AU - Mauduit, Christian

AU - Pomerance, Carl

AU - Sárközy, A.

PY - 2005/3

Y1 - 2005/3

N2 - We give an asymptotic formula for the distribution of those integers n in a residue class, such that n has a fixed sum of base-g digits, with some uniformity over the choice of the modulus and g. We then use this formula to solve the problem of I. Niven of giving an asymptotic formula for the distribution of those integers n divisible by the sum of their base-g digits. Our results also allow us to give a stronger form of a result of M. Olivier dealing with the distribution of integers with a given gcd with their sum of base-g digits.

AB - We give an asymptotic formula for the distribution of those integers n in a residue class, such that n has a fixed sum of base-g digits, with some uniformity over the choice of the modulus and g. We then use this formula to solve the problem of I. Niven of giving an asymptotic formula for the distribution of those integers n divisible by the sum of their base-g digits. Our results also allow us to give a stronger form of a result of M. Olivier dealing with the distribution of integers with a given gcd with their sum of base-g digits.

KW - Niven numbers

KW - Sum-of-digits function

UR - http://www.scopus.com/inward/record.url?scp=24344469702&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=24344469702&partnerID=8YFLogxK

U2 - 10.1007/s11139-005-0824-6

DO - 10.1007/s11139-005-0824-6

M3 - Article

VL - 9

SP - 45

EP - 62

JO - Ramanujan Journal

JF - Ramanujan Journal

SN - 1382-4090

IS - 1-2

ER -