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arXiv · 1901.02650

Primes in arithmetic progressions and nonprimitive roots

Pieter Moree·Min Sha
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Abstract

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

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Pieter Moree, Min Sha. 2019-05-02. Primes in arithmetic progressions and nonprimitive roots. https://doi.org/10.1017/s0004972719000443

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