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

摘要

Let Pr 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 pi with x being a P_6. This result constitutes a refinement upon that of Hooley C.