### Abstract

Let q be a positive integer, let I = I(q) and J = J(q) be subintervals of integers in [1, q] and let M be the set of elements of I that are invertible modulo q and whose inverses lie in J. We show that when q approaches infinity through a sequence of values such that φ(q)/q → 0, the r-spacing distribution between consecutive elements of M becomes exponential.

Original language | English (US) |
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Pages (from-to) | 185-203 |

Number of pages | 19 |

Journal | Proceedings of the Edinburgh Mathematical Society |

Volume | 46 |

Issue number | 1 |

DOIs | |

State | Published - Feb 2003 |

### Keywords

- Exponential sums
- Inverses
- Poissonian distribution

### ASJC Scopus subject areas

- Mathematics(all)

## Fingerprint Dive into the research topics of 'Distribution of gaps between the inverses mod q'. Together they form a unique fingerprint.

## Cite this

Cobeli, C., Vâjâitu, M., & Zaharescu, A. (2003). Distribution of gaps between the inverses mod q.

*Proceedings of the Edinburgh Mathematical Society*,*46*(1), 185-203. https://doi.org/10.1017/S0013091501000724