Waring-Goldbach Problem: Two Squares, Two Cubes and Two Biquadrates

摘要

Let Pr denote an almost-prime with at most r prime factors, counted according to multiplicity. In this paper it is proved that for every sufficiently large even integer N, the equation N=X~2+p_1~2+p_2~3+p_3~3+p_4~4+p_5~4 is solvable with x being an almost-prime P_6 and the p_j (j=1,..., 5) are primes.