一个素变数丢番图不等式

摘要

In this paper we prove that if 1 ＜ c ＜ 14142/8923,|P1+P2+Pa+P4+Pc/5-[＜log-1 Nissolvableinprimenumbersp1,p2,p3,p4,p5forsufficientlylarge N, which extends Piatetski-Shapiro's range 1 ＜c ＜ 1.5. Moreover, we investigate the problem in case of four primes.%本文证明了如果1＜c＜14142/8923,则素变数丢番图不等式|pc1+pc2+pc3+pc4+pc5-N|＜log-1N对充分大的N是可解的,改进了Piatetski-Shapiro的结果1＜c＜1.5.另外,我们也研究了4个素变数丢番图不等式的情形.