The Integral Part of a Nonlinear Form with k Powers of Primes
Wei Ping LI1, Tian Ze WANG2
Author information+
1. Department of Mathematics and Information Science, Henan University of Economics and Law, Zhengzhou 450002, P. R. China;
2. School of Mathematics and Information Science, North China University of Water Conservancy and Electric Power, Zhengzhou 450011, P. R. China
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.
Wei Ping LI, Tian Ze WANG.
The Integral Part of a Nonlinear Form with k Powers of Primes. Acta Mathematica Sinica, Chinese Series, 2013, 56(4): 605-612 https://doi.org/10.12386/A2013sxxb0061
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参考文献
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