### 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 |
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Pages (from-to) | 45-62 |

Number of pages | 18 |

Journal | Ramanujan Journal |

Volume | 9 |

Issue number | 1-2 |

DOIs | |

Publication status | Published - Mar 1 2005 |

### Keywords

- Niven numbers
- Sum-of-digits function

### ASJC Scopus subject areas

- Algebra and Number Theory

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## Cite this

Mauduit, C., Pomerance, C., & Sárközy, A. (2005). On the distribution in residue classes of integers with a fixed sum of digits.

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