A System of Two Diophantine Inequalities with Primes - Xue Han; Huafeng Liu; Deyu Zhang (Journal of Mathematics)
Let 1<d<c<128/119, 1<α<β<61−d/c. In this paper, we prove that there exist positive real numbers N10 and N20 depending on c,d,α,β such that for all real numbers N1>N10, N2>N20 and α≤N2/N1d/c≤β, the system of two Diophantine inequalities p1c+⋯+p6c−N1<N1−1/c128/119−clog109N1,p1d+⋯+p6d−N2<N2−1/d128/119−dlog109N2 is solvable in prime variables p1,…,p6.