One Diophantine inequality with integer and prime variables

被引：1

作者：

Yang, Yongqiang ^{[2
]}

Li, Weiping ^{[1
]}

机构：

[1] Henan Univ Econ & Law, Dept Math & Informat Sci, Zhengzhou 450046, Peoples R China

[2] Henan Univ Econ & Law, Coll Comp & Informat Engn, Zhengzhou 450046, Peoples R China

来源：

JOURNAL OF INEQUALITIES AND APPLICATIONS | 2015年

基金：

中国国家自然科学基金;

关键词：

Davenport-Heilbronn method; prime; Diophantine approximation; APPROXIMATION; NUMBERS;

D O I：

10.1186/s13660-015-0817-y

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, we show that if lambda(1), lambda(2), lambda(3), lambda(4) are positive real numbers, at least one of the ratios lambda(i)/lambda(j) (1 <= i < j <= 4) is irrational, then the inequality vertical bar lambda(1)x(1)(2) + lambda(2)x(2)(3) + lambda(3)x(3)(4) + lambda(4)x(4)(5) - p - 1/2 vertical bar < 1/2 has infinite solutions with natural numbers x(1), x(2), x(3), x(4) and prime p.

引用

页数：9