On the Waring-Goldbach Problem for Six Cubes and Two Biquadrates

Abstract

Let P _r denote an almost prime with at most r prime factors, counted according to multiplicity. In the present paper, it is proved that for any sufficiently large even integer n, the equation $n = {x^3} + p_1^3 + p_2^3 + p_3^3 + p_4^3 + p_5^3 + p_6^4 + p_7^4$ has solutions in primes p _i with x being a P ₆. This result constitutes a refinement upon that of Hooley C.

Keywords

Waring-Goldbach problem / Hardy-Littlewood method / Sieve theory

References

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