Non primitive roots with a prescribed residue pattern

Article Type

Research Article

Publication Title

Proceedings of the Indian Academy of Sciences: Mathematical Sciences

Abstract

Let p be an odd 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. In this paper, for a subset { a1, a2, ⋯ , an} of Z\ { - 1 , 0 , 1 } , we prove each coprime residue class contains a positive density of primes p not having ai as a t-near primitive root and with the ai satisfying a prescribed residue pattern modulo p, for 1 ≤ i≤ n. We also prove a more refined variant of it.

DOI

https://10.1007/s12044-023-00728-4

Publication Date

6-1-2023

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