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Find the smallest positive integer k

Source: Polish MO Round 3 2009,problem 2

November 3, 2009
analytic geometrygeometrypigeonhole principlemodular arithmeticnumber theoryleast common multiplecombinatorics unsolved

Problem Statement

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