Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4594430 | Journal of Number Theory | 2012 | 13 Pages |
Abstract
For given positive integers n and a, let R(n;a) denote the number of positive integer solutions (x,y) of the Diophantine equationan=1x+1y. WriteS(N;a)=ân⩽N(n,a)=1R(n;a). Recently Jingjing Huang and R.C. Vaughan proved that for 4⩽N and a⩽2N, there is an asymptotic formulaS(N;a)=3Ï2aâp|apâ1p+1â
N(log2N+c1(a)logN+c0(a))+Î(N;a). In this paper, we shall get a more explicit expression with better error term for c0(a).
Keywords
Related Topics
Physical Sciences and Engineering
Mathematics
Algebra and Number Theory
Authors
Chaohua Jia,