Wei Ping LI, Tian Ze WANG
Using Davenport-Heilbronn method, this paper shows that if μ1, . . . , μr are non-zero real numbers, not both negative, at least one of μj (1≤ j ≤ r) is irrational, and k,m, r are positive integers satisfying k ≥ 4, r ≥ 2k-1+1, then there exist infinitely many primes p1, . . . , pr, p such that [μ1p1k+···+μrprk]=mp. In particular, [μ1p1k+···+μrprk] represents infinitely many primes.