## Waring-Goldbach problem for unlike powers. II.(Chinese. English summary)Zbl 1121.11312

Summary: In this paper, we are concerned with Waring-Goldbach problems for unlike powers. It is proved that with at most $$O(N^{{47\over48}+\varepsilon})$$ exceptions, all even positive integers up to $$N$$ are expressible in the form $$p^2_2+p^3_3+p^4_4+p^5_5$$.

### MSC:

 11P32 Goldbach-type theorems; other additive questions involving primes 11P05 Waring’s problem and variants 11P55 Applications of the Hardy-Littlewood method

### Keywords:

Waring-Goldbach problem; circle method; exceptional set

Zbl 1128.11043