# Square-full primitive roots

## TL;DR

This paper establishes bounds on the smallest square-full primitive roots modulo a prime using character sum estimates, providing both unconditional and conditional results.

## Contribution

It introduces new bounds for square-full primitive roots modulo primes, improving understanding of their distribution and size.

## Key findings

- Unconditional bound: less than p^{2/3 + 3/(4√e) + ε}
- Conditional bounds are also provided
- Advances the knowledge of primitive root sizes for square-full integers

## Abstract

We use character sum estimates to give a bound on the least square-full primitive root modulo a prime. Specifically, we show that there is a square-full primitive root mod $p$ less than $p^{2/3 + 3/(4 \sqrt{e})+ \epsilon}$, and we give some conditional bounds.