## Exceptional set for sums of unlike powers of primes.(English)Zbl 1443.11204

Summary: Let $$N$$ be a sufficiently large integer. In this paper, it is proved that with at most $$O(N^{13/16+\varepsilon})$$ 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.

### MSC:

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

### Keywords:

Waring-Goldbach problem; circle method; exceptional set
Full Text:

### References:

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