What question did this study set out to answer?

This research aims to prove that every non-square integer other than -1 serves as a primitive root for infinitely many prime numbers.

March 27, 2026Open Access

Artin's Conjecture on Primitive Roots

Key Points

This research aims to prove that every non-square integer other than -1 serves as a primitive root for infinitely many prime numbers.
Proof development using number theoretical concepts
Analysis of non-square integers and their properties relative to primes
Every non-square integer except for -1 is shown to be a primitive root modulo infinitely many primes.

Abstract

Preprint v1 — A proof that every non-square integer other than -1 is a primitive root modulo infinitely many primes. Abstract redacted pending IP review. Full abstract and unrestricted access will be available in v2 upon completion of intellectual property proceedings. Author: Joseph Keen Affiliation: Phoenix Quantum Labs LLC

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Cite This Study

Joseph R. Keen (Wed,) studied this question.

synapsesocial.com/papers/69c620d515a0a509bde19814 https://doi.org/https://doi.org/10.5281/zenodo.19216570