关于两个素数和一个素数k次幂的丢番图不等式

A Diophantine Inequality with Two Primes and One k-th Power of a Prime

令■设λ1,λ2,λ3是不全同号的非零实数,且满足λ1/λ2为无理数,则对于任意实数η和ε> 0,不等式■有无穷多组素数解p1,p2,p3.该结果改进了Gambini,Languasco和Zaccagnini的结果.

Let ■Suppose that λ1,λ2 and λ3 axe non-zero real numbers,not all of the same sign,satisfying that λ1/λ2 is irrational.Then for any real number η and ε> 0,the inequality ■has infinitely many solutions in prime variables p1,p2,p3.This result constitutes an improvement on that of Gambini,Languasco and Zaccagnini.