Chinese Quarterly Journal of Mathematics ›› 2013, Vol. 28 ›› Issue (3): 317-322.

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

  

  1. 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

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 

CLC Number: