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.

中文翻译：

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素数异次幂之和的特殊集合（II）

令N为足够大的整数。在本文中，证明了，最多具有\（O（N ^ {7/18 + \ varepsilon}）\）个异常，直到N的所有偶数正整数都可以用\（p_1 ^ 2 + p_2 ^ 2 + p_3 ^ 3 + p_4 ^ 3 + p_5 ^ 4 + p_6 ^ 4 \），其中\（p_1，p_2，p_3，p_4，p_5，p_6 \）是质数，这是对以前工作的改进。