On a property of 2-dimensional integral Euclidean lattices (Q661961)

A lattice in \(d\)-dimensional Euclidean space is called \textit{universally concyclic}, if for every integer \(n\geq 0\) there is a \(d-1\)-dimensional spherical surface that passes through exactly \(n\) lattice points. The paper shows that all integral lattices of dimension \(d\geq 2\) are universally concyclic. For the 2-dimensional case, the authors use the well known correspondence between 2-dimensional integral lattices and orders in imaginary quadratic number fields and construct the circle as a translate of a suitable norm equation.