The least primitive root modulo $p^{2}$

TL;DR

This paper establishes an explicit upper bound for the smallest primitive root modulo p^2, demonstrating that for every prime p, such a primitive root exists below p^{0.99}, advancing understanding of primitive roots in number theory.

Contribution

The paper provides a new explicit estimate for the least primitive root modulo p^2, showing it is less than p^{0.99} for all primes p, which improves previous bounds.

Findings

Every prime p has a primitive root mod p^2 less than p^{0.99}.

Provides an explicit estimate on the least primitive root modulo p^2.

Advances bounds on primitive roots in number theory.

Abstract

We provide an explicit estimate on the least primitive root mod $p^{2}$. We show, in particular, that every prime $p$ has a primitive root mod $p^{2}$ that is less than $p^{0.99}$.