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Math Help - Lattice Points

  1. #1
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    Lattice Points

    Hey, the following is meant to be an application of the Chinese Remainder Theorem.

    A lattice point in the plane is a point (m,n), where m and n are integers.
    A point (m,n) \in \mathbb{Z}^2 is called invisible if the straight line segment from (0,0) to (m,n) goes through some other integer lattice point.
    Show that for every M > 0 there exists a square in \mathbb{Z}^2 of side length M, so that all its lattice points are invisible.
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  2. #2
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    Quote Originally Posted by EinStone View Post
    Hey, the following is meant to be an application of the Chinese Remainder Theorem.

    A lattice point in the plane is a point (m,n), where m and n are integers.
    A point (m,n) \in \mathbb{Z}^2 is called invisible if the straight line segment from (0,0) to (m,n) goes through some other integer lattice point.
    Show that for every M > 0 there exists a square in \mathbb{Z}^2 of side length M, so that all its lattice points are invisible.
    EDIT:
    Found the proof here, so the problem is solved.
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