  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.
