Each integer coordinates are colored with one color and at least 5 colors are used to color every integer coordinates. Two integer coordinates (x,y) and (z,w) are colored in the same color if x−z and y−w are both multiples of 3. Prove that there exists a line that passes through exactly three points when five points with different colors are chosen randomly. algebraic geometrycombinatorical geometrycombinatoricsKJMOColoring