刊名:Journal of Mathematical Analysis and Applications
出版年:2016
出版时间:1 August 2016
年:2016
卷:440
期:1
页码:145-154
全文大小:301 K
文摘
Let (ai,aj)=1, 1≤i<j≤s and s=2k+1, where a1,⋯,as,s and k≥4 are nonzero integers. In this paper, we show that if the diagonal diophantine equation is satisfying some necessary conditions, then we have the following results: For any ϵ>0, we have
(i)
if a1,⋯,as are not all of the same sign, then the above equation has solutions in primes pj satisfying pj≪|n|1/k+A3⋅2k−1+ϵ,
(ii)
if a1,⋯,as are all positive, then the above equation is solvable in prime pj whenever n≫A3k⋅2k−1+1+ϵ.
This result is the general case of the Diophantine equations with Small Prime Variables.