Exceptional set for sums of unlike powers of primes (II)

Abstract

Let N be a sufficiently large integer. In this paper, it is proved that, with at most $$O(N^{7/18+\varepsilon })$$ exceptions, all even positive integers up to N can be represented in the form $$p_1^2+p_2^2+p_3^3+p_4^3+p_5^4+p_6^4$$ , where $$p_1,p_2,p_3,p_4,p_5,p_6$$ are prime numbers, which constitutes an improvement over some previous work.