A note on the inverse problem for the lattice points

Details A note on the inverse problem for the lattice points A note on the inverse problem for the lattice points

2010-06-29

arxiv.org/abs/1006.5740v4

Mathematics

Number Theory

v2 information on funding added for second author v3 contact information updated v4 information on funding corrected and bibli

Scientific paper

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.

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