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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 theinteger points of the difference set of $K$, $(K-K)\cap\mathbb{Z}^2$, is notcontained on the coordinate axes,$\mathbb{Z}\times\{0\}\cup\mathbb{Z}\times\{0\}$. This result gives a negativeanswer to a question posed by P. Hegarty and M. Nathanson on relatively primelattice points.

A note on the inverse problem for the lattice points