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arXiv · 2610.28774

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

Yuhua Zhao·Jinjiang Li·Linji Long·Min Zhang
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Abstract

Let $N$ be a sufficiently large real number. In this paper, it is proved that, for $1 0$, 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 each of the numbers $p_i+2\,(i=1,2,3,4)$ has, counted according to multiplicity, at most $[\frac{31250}{5179-3909c}]$ prime factors, which constitutes a large improvement upon the previous results of Dimitrov [13] and Li-Xue-Zhang [22], respectively.

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Yuhua Zhao, Jinjiang Li, Linji Long, Min Zhang. 2026-10-20. A quaternary Diophantine inequality with prime numbers of a special form (II). https://arxiv.org/abs/2610.28774

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