数学季刊 ›› 2008, Vol. 23 ›› Issue (1): 1-7.

• •    下一篇

一个混合幕为2和4的丢番图不等式

  

  1. 1. Department of Mathematics,Tongji University  2. College of Information,Henan University of Finance and Economics 

  • 收稿日期:2004-06-04 出版日期:2008-03-30 发布日期:2023-10-10
  • 作者简介: GONG Ke(1980-), male, native of Tanghe, Henan, Ph.D., engages in number theory; LI Wei- ping(1972-), male, native of Fugou, Henan, a lecturer of Henan University of Finance and Economics, Ph.D., engages in number theory.
  • 基金资助:
    Supported by the National Natural Science Foundation of China(10671056)

One Additive Diophantine Inequality with Mixed Powers 2 and 4

  1. 1. Department of Mathematics,Tongji University  2. College of Information,Henan University of Finance and Economics 
  • Received:2004-06-04 Online:2008-03-30 Published:2023-10-10
  • Contact:
  • About author: GONG Ke(1980-), male, native of Tanghe, Henan, Ph.D., engages in number theory; LI Wei- ping(1972-), male, native of Fugou, Henan, a lecturer of Henan University of Finance and Economics, Ph.D., engages in number theory.
  • Supported by:
    Supported by the National Natural Science Foundation of China(10671056)

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摘要： In this paper, it is shown that: if λ1,…,λ8 are nonzero real numbers, not all of the same sign, such that λ1/λ2 is irrational, then for any real numberηandε>0 the inequality |λ1x12+λ2x22+λ3x34+…+λ8x84+η|<ε has infinitely many solutions in positive integers x1,…,x8.

关键词: Diophantine inequality, mixed powers, circle method

Abstract: In this paper, it is shown that: if λ1,…,λ8 are nonzero real numbers, not all of the same sign, such that λ1/λ2 is irrational, then for any real numberηandε>0 the inequality |λ1x12+λ2x22+λ3x34+…+λ8x84+η|<ε has infinitely many solutions in positive integers x1,…,x8.

Key words: Diophantine inequality, mixed powers, circle method

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