Number of solutions in a box of a linear equation in an Abelian group
Volume 143 / 2016
Colloquium Mathematicum 143 (2016), 17-22
MSC: Primary 11D79; Secondary 20K01.
DOI: 10.4064/cm6145-12-2015
Published online: 3 December 2015
Abstract
For every finite Abelian group $\varGamma $ and for all $g,a_1,\ldots ,a_k\in \varGamma ,$ if there exists a solution of the equation $\sum _{i=1}^k a_ix_i = g$ in non-negative integers $x_i\le b_i,$ where $b_i$ are positive integers, then the number of such solutions is estimated from below in the best possible way.
