Primes in arithmetic progressions and nonprimitive roots

Pieter Moree, Min Sha*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

2 Citations (Scopus)


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 languageEnglish
Pages (from-to)388-394
Number of pages7
JournalBulletin of the Australian Mathematical Society
Issue number3
Publication statusPublished - Dec 2019


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


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