Exceptional Set for Sums of Symmetric Mixed Powers of Primes

Authors :: Min Zhang
Jinjiang Li
Zhuo Zhang
Chao Liu
Source :: Symmetry, Volume 12, Issue 3, Symmetry, Vol 12, Iss 3, p 367 (2020)
Publication Year :: 2020
Publisher :: Multidisciplinary Digital Publishing Institute, 2020.
Abstract: The main purpose of this paper is to use the Hardy&ndash<br />Littlewood method to study the solvability of mixed powers of primes. To be specific, we consider the even integers represented as the sum of one prime, one square of prime, one cube of prime, and one biquadrate of prime. However, this representation can not be realized for all even integers. In this paper, we establish the exceptional set of this kind of representation and give an upper bound estimate.