On a ternary diophantine inequality with prime numbers of a special type II

Pub Date : 2024-07-02 DOI:10.1007/s10998-024-00602-4

Li Zhu

引用次数: 0

Abstract

Suppose that N is a sufficiently large real number and E is an arbitrarily large constant. In this paper, it is proved that, for $1< c < \frac{7}{6}$, the Diophantine inequality

$$\begin{aligned} |p_1^c+p_2^c+p_3^c-N|<(\log N)^{-E} \end{aligned}$$

is solvable in prime variables $p_1,p_2,p_3$ so that each of the numbers $p_i+2,\,i=1,2,3$, has at most $\big [3.43655+{\frac{12.12}{7-6c}}\big ]$ prime factors counted with multiplicity.

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关于有特殊类型素数 II 的三元二叉不等式

假设 N 是一个足够大的实数，E 是一个任意大的常数。本文证明，对于 $1< c < \frac{7}{6}$, Diophantine 不等式 $$\begin{aligned}.|p_1^c+p_2^c+p_3^c-N|<(\log N)^{-E}\end{aligned}$$在素数变量 $p_1,p_2,p_3$中是可解的，因此每个数 $p_i+2,\,i=1,2,3$，最多有$\big [3.43655+{frac{12.12}{7-6c}}\big ]$以倍数计算的素因子。

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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