Density of Squarefree Totients $p-1$ and Primitive Roots

TL;DR

This paper derives an effective asymptotic formula for counting prime numbers p where p-1 is squarefree and p has a fixed primitive root u, advancing understanding of primitive roots and totient properties.

Contribution

It provides the first effective asymptotic formula for the distribution of squarefree totients with a fixed primitive root.

Findings

Established an explicit asymptotic count for such primes.

Identified conditions on primitive roots for the asymptotic formula.

Enhanced understanding of primitive root distribution in relation to squarefree totients.

Abstract

This note determines an effective asymptotic formula for the number of squarefree totients $p-1$ with a fixed primitive root $u\ne \pm 1, v^2$.