幂次为2,3,4,5的素变量非线性型的整数部分

The Integer Part of Nonlinear Form with Mixed Powers 2,3,4,5 and Prime Variables

考虑了一个混合幂次为2，3，4，5的素变量非线性型的整数部分表示无穷多素数的问题.运用Davenport-Heilbronn方法证明了：如果λ1，λ2，λ3，λ4是正实数，至少有一个λi/λj（1≤i〈 j≤4）是无理数，那么存在无穷多素数p1，p2，p3，p4，p，使得[λ1p12＋λ2p23＋λ3p34＋λ4p45]=p.

The present paper considered one problem which integer part of nonlinear form with mixed powers 2, 3, 4, 5 and prime variables represents prime infinitely. Using Davenport-Heilbronn method, we show that if λ1,λ2,λ3,λ4 are positive real numbers,at least one of the ratios λi/λj （1≤i〈 j≤4） is irrational, then there exist infinitely many primes p1,p2,p3,p4,p such that[λ1p12＋λ2p23＋λ3p34＋λ4p45]=p.