%0 Journal Article
%T Restricted linear congruences
%A Khodakhast Bibak
%A Bruce M. Kapron
%A Venkatesh Srinivasan
%A Roberto Tauraso
%A L¨¢szl¨® T¨®th
%J Mathematics
%D 2015
%I arXiv
%X In this paper, using properties of Ramanujan sums and of the discrete Fourier transform of arithmetic functions, we give an explicit formula for the number of solutions of the linear congruence $a_1x_1+\cdots +a_kx_k\equiv b \pmod{n}$, with $\gcd(x_i,n)=t_i$ ($1\leq i\leq k$), where $a_1,t_1,\ldots,a_k,t_k, b,n$ ($n\geq 1$) are arbitrary integers. Some special cases of this problem have been already studied in many papers. The problem is very well-motivated and in addition to number theory has intriguing applications in combinatorics, computer science, and cryptography, among other areas.
%U http://arxiv.org/abs/1503.01806v2