Suppose that c,d,α,β,are real numbers satisfying 1<d<c<14=13,1<α<β<6^(1−d=c).In this paper,we prove that there exist numbers N_(1)^((0))and N_(2)^((0)),depending on c,d,α,β,such that for all re...Suppose that c,d,α,β,are real numbers satisfying 1<d<c<14=13,1<α<β<6^(1−d=c).In this paper,we prove that there exist numbers N_(1)^((0))and N_(2)^((0)),depending on c,d,α,β,such that for all real numbers N1_(1)and N_(2)satisfying N_(1)>N_(1)^((0)),N_(2)>N_(2)^((0))andα≤N_(2)/N_(1)^(d=c)≤β,the system of two Diophantine inequalities|p_^(1)+…+p_(6)^(c)-N_(1)|<N_(1)^(−(1=c)(14=13−c))logN_(1),|p_(1)^(d)+…+p_(6)^(d)|N_(2)^(−(1=d)(14=13−d))logN_(2)has solutions in prime variables p_(1)…,p6.展开更多
文摘Suppose that c,d,α,β,are real numbers satisfying 1<d<c<14=13,1<α<β<6^(1−d=c).In this paper,we prove that there exist numbers N_(1)^((0))and N_(2)^((0)),depending on c,d,α,β,such that for all real numbers N1_(1)and N_(2)satisfying N_(1)>N_(1)^((0)),N_(2)>N_(2)^((0))andα≤N_(2)/N_(1)^(d=c)≤β,the system of two Diophantine inequalities|p_^(1)+…+p_(6)^(c)-N_(1)|<N_(1)^(−(1=c)(14=13−c))logN_(1),|p_(1)^(d)+…+p_(6)^(d)|N_(2)^(−(1=d)(14=13−d))logN_(2)has solutions in prime variables p_(1)…,p6.
