### 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 |
---|---|

Pages (from-to) | 45-62 |

Number of pages | 18 |

Journal | Ramanujan Journal |

Volume | 9 |

Issue number | 1-2 |

DOIs | |

Publication status | Published - Mar 2005 |

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### Keywords

- Niven numbers
- Sum-of-digits function

### ASJC Scopus subject areas

- Algebra and Number Theory

### Cite this

*Ramanujan Journal*,

*9*(1-2), 45-62. https://doi.org/10.1007/s11139-005-0824-6

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

Research output: Contribution to journal › Article

*Ramanujan Journal*, vol. 9, no. 1-2, pp. 45-62. https://doi.org/10.1007/s11139-005-0824-6

}

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 -