Primes in arithmetic progressions and nonprimitive roots

Pieter Moree; Min Sha

doi:10.1017/S0004972719000443

Primes in arithmetic progressions and nonprimitive roots

Pieter Moree, Min Sha^*

^*Corresponding author for this work

School of Computing

Research output: Contribution to journal › Article › peer-review

1 Citation (Scopus)

Abstract

Let p be a prime. If an integer g generates a subgroup of index t in (Z/pZ)*, then we say that g is a t-near primitive root modulo p. We point out the easy result that each coprime residue class contains a subset of primes p of positive natural density which do not have g as a t-near primitive root and we prove a more difficult variant.

Original language	English
Pages (from-to)	388-394
Number of pages	7
Journal	Bulletin of the Australian Mathematical Society
Volume	100
Issue number	3
DOIs	https://doi.org/10.1017/S0004972719000443
Publication status	Published - Dec 2019

Keywords

primitive root
near-primitive root
Artin's primitive root conjecture
arithmetic progression
secondary 11N69
2010 Mathematics subject classification
primary 11N13

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10.1017/S0004972719000443

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abstract = "Let p be a prime. If an integer g generates a subgroup of index t in (Z/pZ)*, then we say that g is a t-near primitive root modulo p. We point out the easy result that each coprime residue class contains a subset of primes p of positive natural density which do not have g as a t-near primitive root and we prove a more difficult variant.",

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KW - near-primitive root

KW - Artin's primitive root conjecture

KW - arithmetic progression

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KW - 2010 Mathematics subject classification

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SN - 0004-9727

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Primes in arithmetic progressions and nonprimitive roots

Abstract

Keywords

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