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