ASU 457 All Soviet Union MO 1987 lattice point, vectors, marked points
Source:
August 7, 2019
vectorcombinatoricslattice pointscombinatorial geometry
Problem Statement
Some points with the integer coordinates are marked on the coordinate plane. Given a set of nonzero vectors. It is known, that if you apply the beginnings of those vectors to the arbitrary marked point, than there will be more marked ends of the vectors, than not marked. Prove that there is infinite number of marked points.