幂次为2和3的整变量非线性型的整数部分  

Integral Part of a Nonlinear Form with Square and Cube

作　　者：寇晨阳 KOU Chen-yang(School of Mathematics and Statistics,North China University of Water Resources and Electric Power,Zhengzhou 450046,China)

机构地区：[1]华北水利水电大学数学与统计学院,河南郑州450046

出　　处：《兰州文理学院学报（自然科学版）》2023年第3期1-7,共7页Journal of Lanzhou University of Arts and Science(Natural Sciences)

摘　　要：用DavenportGHeilbronn方法证明了混合幂次为2,3,3的素变量非线性型的整数部分表示无穷多素数的问题:假设λ_(1),λ_(2),λ_(3)是非零实数,至少有一个λi/λj(1≤i<j≤3)为无理数,x1,x2,x3是正整数,那么λ_(1)x2^(1)+λ_(2)x3^(2)+λ_(3)x3^(3)的整数部分可表示无穷多素数.In this paper,the Davenport-Heilbronn method is used to prove that the integer part of the nonlinear type of prime variable with mixed powers of 2,3,3 represents infinitely many primes.We show that if λ_(1),λ_(2),λ_(3) are non-zero real numbers,and at least one of the numbersλ/λj(1≤i<j≤3)is irrational,then the integer parts of λ_(1) x 2^(1)+λ_(2) x 3^(2)+λ_(3) x 3^(3) are prime infinitely often for integers x 1,x 2,x 3.

关 键 词：素数变量 丢番图逼近 Davenport-Heilbronn方法 

分 类 号：O156.4[理学—数学]