Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
8896933 | Journal of Number Theory | 2018 | 11 Pages |
Abstract
Consider the linear congruence equationa1sx1+â¦+aksxkâ¡b(mod ns) where ai,bâZ,sâN. Denote by (a,b)s the largest lsâN which divides a and b simultaneously. Given ti|n, we seek solutions ãx1,â¦,xkãâZk for this linear congruence with the restrictions (xi,ns)s=tis. Bibak et al. [2] considered the above linear congruence with s=1 and gave a formula for the number of solutions in terms of the Ramanujan sums. In this paper, we derive a formula for the number of solutions of the above congruence for arbitrary sâN which involves the generalized Ramanujan sums defined by E. Cohen [5].
Related Topics
Physical Sciences and Engineering
Mathematics
Algebra and Number Theory
Authors
K. Vishnu Namboothiri,