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"相关结果 30条Let $p \geq 2$ be a large prime, and let $k \ll \log p $ be a small integer. This note proves the existence of various configurations of $(k+1)$-tuples of consecutive and quasi consecutive primitive roots $n+a_0, n+a_1, n+a_2, \ldots, n+a_k$ in the finite field $\mathbb{F}_p$, where $a_0,a_1, \ldots, a_k$ is a fixed $(k+1)$-tuples of distinct integers.
arxiv.orgThis note presents an upper bound for the least prime primitive roots $g^*(p)$ modulo $p$, a large prime. The current literature has several estimates of the least prime primitive root $g^*(p)$ modulo a prime $p\geq 2$ such as $g^*(p)\ll p^c, c>2.8$. The estimate provided within seems to sharpen this estimate to the smaller estimate $g^*(p)\ll p^{5/\log \log p}$ uniformly for all large primes $p\geq 2$.
arxiv.org