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Published online by Cambridge University Press: 24 October 2008
Blichfeldt (2) gave a method of proving the existence of lattice points in certain regions. His method depends on the following lemma (which he stated in a somewhat different form):
Lemma 1. Let K′ be a closed region of volume V. Let K be another region so related to K′ that the difference of any two points in K′ is a point in K. Let Λ be any lattice whose determinant is positive and does not exceed V.