4 ms·

It doesn't hold. Pick (0,1), (0,2), (0,3), (0,4), (0,5) on the plane z = 0

• jonsen 14y ago
  Well, you have five integer points on the same line.
  • fahadkhan 14y ago
    "Suppose we arbitrarily choose 5 integer points in a plane. Show that we can always find 2 among these 5 integer points such that the line segment joining the 2 points contains at least 1 more integer point." I am not sure what you mean. I have 'arbitrarily' picked 5 integer points on a plane. Yes, they happen to lie on line. All their line segments contain only these integer points. Perhaps you mean that is line not on "a plane"? In that case (0,0), (0,1), (0,2), (0,3), (0,1) is another counter example.
    • vbuterin 14y ago
      In the case of {(0,0),(0,2)}, (0,1) counts as "1 more integer point" - the point has to be not one of the two points generating the line, not a point outside the set of 5 points on the plane.
  • fahadkhan 14y ago
    Or is my assumption "more" means an integer point not in the set of five selected wrong?
    • jonsen 14y ago
      Yes, it's wrong. It means at least one integer point more than the two integer end points (which of course have to be on the line).