### Abstract

Many results have been proved on the distribution of the primitive roots. These results reflect certain random type properties of the set G_{p} of the primitive roots modulo p. This fact motivates the question that in what extent behaves G_{p} as a random subset of ℤ_{p}? First a much more general form of this problem is studied by using the notion of pseudo-randomness of subsets of ℤ_{n} which has been introduced and studied recently by Dartyge and Sárközy. This is followed by the study of the pseudo-randomness of a subset of ℤ_{p} defined by index properties. In both cases it turns out that these subsets possess strong pseudo-random properties (the well-distribution measure and correlation measure of order k are small) but the pseudo-randomness is not perfect: there is a pseudo-random measure (the symmetry measure) which is large.

Original language | English |
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Pages (from-to) | 139-162 |

Number of pages | 24 |

Journal | Combinatorica |

Volume | 30 |

Issue number | 2 |

DOIs | |

Publication status | Published - Sep 24 2010 |

### ASJC Scopus subject areas

- Discrete Mathematics and Combinatorics
- Computational Mathematics

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## Cite this

*Combinatorica*,

*30*(2), 139-162. https://doi.org/10.1007/s00493-010-2534-y