2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/66728Given $A\in \Z^{m\times n}$ 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.9 pages; ICCSA 2003 conference, Montreal, May 2003CombinatoricsAlgebraic Geometry90C10; 90C05; 52C07text