On the least square-free primitive root modulo $p$

TL;DR

This paper establishes an upper bound of p^{0.96} for the smallest square-free primitive root modulo p, improving understanding of primitive roots in number theory.

Contribution

It proves a new upper bound for the least square-free primitive root modulo p, advancing previous bounds in number theory research.

Findings

g^{ ext{square}}(p) < p^{0.96} for all primes p

Provides a significant improvement over previous bounds

Enhances understanding of primitive roots and their properties

Abstract

Let $g^{\square}(p)$ denote the least square-free primitive root modulo $p$. We show that $g^{\square}(p)< p^{0.96}$ for all $p$.