Square-full primitive roots

Marc Munsch, Tim Trudgian

Published 2017-03-15Version 1

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.