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Sponsored AI Networking Cookbook: Practical recipes for AI-assisted network automation and development AI Networking Cookbook: Practical recipes for AI-assisted network automation and development

Author

Li Long

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Preprint Oct 2026

A quaternary Diophantine inequality with prime numbers of a special form (II)

Let $N$ be a sufficiently large real number. In this paper, it is proved that, for $1<c<\frac{5179}{3909}$ and for any arbitrary large number $E>0$, the Diophantine inequality \begin{equation*} \big|p_1^c+p_2^c+p_3^c+p_4^c-N\big|<(\log N)^{-E} \end{equation*} is solvable in prime variables $p_1,p_2,p_3,p_4$ such that e...

Yu-Hui Zhao, Jin-Jia Li, Li Long et al. · 0 citations
Open access Aug 2026

On Piatetski–Shapiro primes from almost primes

Denote by Pr\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathcal {P}_r$$\end{document} an almost–prime with at most r prime factors, c...

Yu-Hui Zhao, Jin-Jia Li, Li Long et al. · 0 citations

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