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+p1^3+p2^3+p3^3+p...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+p1^3+p2^3+p3^3+p4^3+p1^3+p5^3+p6^3+p7^3 has solutions in primes pi with x being a P6. This result constitutes a refinement upon that of Hooley C.展开更多
基金supported by the National Natural Science Foundation of China(No.11201107)the China Scholarship Council
文摘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+p1^3+p2^3+p3^3+p4^3+p1^3+p5^3+p6^3+p7^3 has solutions in primes pi with x being a P6. This result constitutes a refinement upon that of Hooley C.