混合幂次为2和4的整数变量非线性型的整数部分

数学季刊 ›› 2013, Vol. 28 ›› Issue (3): 317-322.

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混合幂次为2和4的整数变量非线性型的整数部分

1. Department of Mathematics and Information Sciences, Henan University of Economics and Law2. School of Mathematics and Information Sciences, North China University of Water Conservancy and Electric Power

收稿日期:2011-12-07 出版日期:2013-09-30 发布日期:2023-02-21
作者简介:LI Wei-ping(1972-), male, native of Zhoukou, Henan, an associate professor of Henan University of Economics and Law, Ph.D., engages in analytic number theory.
基金资助:
Supported by the NNSF of China(11071070,11371122)； Supported by the Science Research Plan of Education Department of Henan Province(2011B110002)； Supported by the Innovation Scientists and Technicians Troop Construction Projects of Henan Province

The Integer Parts of a Nonlinear Form with Integer Variables and Mixed Powers 2 and 4

1. Department of Mathematics and Information Sciences, Henan University of Economics and Law2. School of Mathematics and Information Sciences, North China University of Water Conservancy and Electric Power

Received:2011-12-07 Online:2013-09-30 Published:2023-02-21
About author:LI Wei-ping(1972-), male, native of Zhoukou, Henan, an associate professor of Henan University of Economics and Law, Ph.D., engages in analytic number theory.
Supported by:
Supported by the NNSF of China(11071070,11371122)； Supported by the Science Research Plan of Education Department of Henan Province(2011B110002)； Supported by the Innovation Scientists and Technicians Troop Construction Projects of Henan Province

摘要/Abstract

摘要： _{The present paper proved that if λ1, λ2, λ3 are positive real numbers, λ1/λ2 is irrational. Then, the integer parts of λ1x21+λ2x22+λ3x43 are prime infinitely often for natural numbers x1, x2, x3.}

关键词: integer variables, diophantine approximation, Davenport-Heilbronn method

Abstract: The present paper proved that if λ1, λ2, λ3 are positive real numbers, λ1/λ2 is irrational. Then, the integer parts of λ1x21+λ2x22+λ3x43 are prime infinitely often for natural numbers x1, x2, x3.

Key words: integer variables, diophantine approximation, Davenport-Heilbronn method

中图分类号:

O156.4

李伟平, 戈文旭, 王天泽. 混合幂次为2和4的整数变量非线性型的整数部分[J]. 数学季刊, 2013, 28(3): 317-322.

LI Wei-ping, GE Wen-xu, WANG Tian-ze. The Integer Parts of a Nonlinear Form with Integer Variables and Mixed Powers 2 and 4[J]. Chinese Quarterly Journal of Mathematics, 2013, 28(3): 317-322.

混合幂次为2和4的整数变量非线性型的整数部分

The Integer Parts of a Nonlinear Form with Integer Variables and Mixed Powers 2 and 4

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