On a linear homogeneous congruence
Volume 106 / 2006
Colloquium Mathematicum 106 (2006), 283-292
MSC: Primary 11D79.
DOI: 10.4064/cm106-2-8
Abstract
The number of solutions of the congruence $a_1x_1+\cdots+a_kx_k\equiv 0\pmod n $ in the box $0\le x_i\le b_i$ is estimated from below in the best possible way, provided for all $i,j$ either $(a_i,n)\,|\, (a_j,n)$ or $ (a_j,n)\,|\, (a_i,n)$ or $n\,|\, [a_i,a_j]$.
