素数k次方和的非线性型的整数部分

The Integral Part of a Nonlinear Form with k Powers of Primes

运用Dawmport-Heilbronn方法证明了:如果μ_1…,μ_r是不全为负的非零实数,至少一个μ_j(1≤j≤r)是无理数,k,m,r是正整数,k≥4,r≥2^(k-1)+1,则存在无穷多素数p_1,…,p_r,p,使得[μ_1p_1~k+…+μ_rp_r^k]=mp.特别地,[μ_1p_1~k+…+μ_rp_r^k]可表示无穷多素数.

Using Davenport Heilbronn method, this paper shows that if μ_1…,μ_r are non-zero real numbers, not both negative, at least one ofμ_1…,μ_r is irrational, and k, m, r are positive integers satisfyingk≥4,r≥2^（k-1）＋1, then there exist infinitely many primes p_1,…,p_r,p,such that [μ_1p_1~k＋…＋μ_rp_r^k]=mp.. In particular,[μ_1p_1~k＋…＋μ_rp_r^k] represents infinitely many primes.