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arXiv · 2509.19309

Small Prime Primitive Roots in Arithmetic Progressions

N. A. Carella
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Abstract

Let $p>1$ be a large prime number, let $q=O(\log\log p)$ and let $1\leq a<q$ be a pair of relatively prime integers. It is proved that there is a prime primitive root $u\ll (\log p)(\log \log p)^5$ such that $u\equiv a\bmod q$ in the prime finite field $\mathbb{F}_p$.

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N. A. Carella. 2025-09-07. Small Prime Primitive Roots in Arithmetic Progressions. https://arxiv.org/abs/2509.19309

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