## Abstract

Let ℙ_{q} be the finite field with q elements and let A denote the . ring of polynomials in one variable with coefficients in ℙ_{q}. Let P be a monic polynomial irreducible in A. We obtain a bound for the least degree of a monic polynomial irreducible in A (q odd) which is a quadratic non-residue modulo P. We also find a bound for the least degree of a monic polynomial irreducible . in A which is a primitive root modulo P.

Original language | English |
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Pages (from-to) | 647-652 |

Number of pages | 6 |

Journal | Proceedings of the American Mathematical Society |

Volume | 126 |

Issue number | 3 |

DOIs | |

Publication status | Published - 1998 |

## Keywords

- Primitive roots
- Quadratic non-residues
- Riemann Hypothesis

## ASJC Scopus subject areas

- General Mathematics
- Applied Mathematics

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