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Lattice points of the plane

Source: IMO Longlist 1989, Problem 27

September 18, 2008
calculusintegrationmodular arithmeticnumber theoryrelatively primecombinatorics unsolvedcombinatorics

Problem Statement

Let L L denote the set of all lattice points of the plane (points with integral coordinates). Show that for any three points A,B,C A,B,C of L L there is a fourth point D, D, different from A,B,C, A,B,C, such that the interiors of the segments AD,BD,CD AD,BD,CD contain no points of L. L. Is the statement true if one considers four points of L L instead of three?
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