## Abstract

Let (FORMULA PRESENTED), A, B be rational integers and for (FORMULA PRESENTED). The sequence (un) is clearly periodic modulo m and we say that (un) is uniformly distributed modulo m if for every 5, every residue modulo m occurs the same number of times in the sequence of residues (FORMULA PRESENTED), where N is the period of (u_{n}) modulo m. If (u_{n}) is uniformly distributed modulo m then m divides N, so we write N=mf. Several authors have characterized those m for which (u_{n}) is uniformly distributed modulo m. In fact in this paper we will show that a much stronger property holds when m = p^{k}, p a prime. Namely, if (u_{n}) is uniformly distributed modulo p^{k} with period p^{k}f, then every residue modulo p^{k} appears exactly once in the sequence (FORMULA PRESENTED), for every s. We also characterize those composite m for which this more stringent property holds.

Original language | English (US) |
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Pages (from-to) | 37-45 |

Number of pages | 9 |

Journal | Transactions of the American Mathematical Society |

Volume | 301 |

Issue number | 1 |

DOIs | |

State | Published - May 1987 |

## ASJC Scopus subject areas

- Mathematics(all)
- Applied Mathematics