算术级数中的小质数 k 次幂残差和非残差

arXiv - MATH - General Mathematics Pub Date : 2024-05-21 DOI:arxiv-2405.13159

N. A. Carella

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摘要

让 $p$ 是一个大奇素数，让 $x=(\log p)^{1+\varepsilon}$ 并且让 $q\ll\log\log p$ 是一个整数，其中 $\varepsilon>0$ 是一个小数。本注无条件地证明了在算术级数 $a+qm\ll x$ 中存在相对质数$1\leq a本文章由计算机程序翻译，如有差异，请以英文原文为准。

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Small Prime $k$th Power Residues and Nonresidues in Arithmetic Progressions

Let $p$ be a large odd prime, let $x=(\log p)^{1+\varepsilon}$ and let $q\ll\log\log p$ be an integer, where $\varepsilon>0$ is a small number. This note proves the existence of small prime quadratic residues and prime quadratic nonresidues in the arithmetic progression $a+qm\ll x$, with relatively prime $1\leq a

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arXiv - MATH - General Mathematics

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