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

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.