Let S be a set of all points of a plane whose coordinates are integers. Find the smallest positive integer k for which there exists a 60-element subset of set S with the following condition satisfied for any two elements A,B of the subset there exists a point C contained in S such that the area of triangle ABC is equal to k . analytic geometrygeometrypigeonhole principlemodular arithmeticnumber theoryleast common multiplecombinatorics unsolved