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 language English 45-62 18 Ramanujan Journal 9 1-2 https://doi.org/10.1007/s11139-005-0824-6 Published - Mar 2005

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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.
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