  Let $K\subseteq\mathbb{R}^2$ be a compact set such that
$K+\mathbb{Z}^2=\mathbb{R}^2$. We prove, via Algebraic Topology, that the
integer points of the difference set of $K$, $(K-K)\cap\mathbb{Z}^2$, is not
contained on the coordinate axes,
$\mathbb{Z}\times\{0\}\cup\mathbb{Z}\times\{0\}$. This result gives a negative
answer to a question posed by P. Hegarty and M. Nathanson on relatively prime
lattice points.
