%0 Journal Article
%T A discrete Farkas lemma
%A Jean B. Lasserre
%J Mathematics
%D 2003
%I arXiv
%X Given $A\in \Z^{m\times n}$ and $b\in\Z^m$, we consider the issue of existence of a nonnegative integral solution $x\in \N^n$ to the system of linear equations $Ax=b$. We provide a discrete and explicit analogue of the celebrated Farkas lemma for linear systems in $\R^n$ and prove that checking existence of integral solutions reduces to solving an explicit linear programming problem of fixed dimension, known in advance.
%U http://arxiv.org/abs/math/0303094v1