# Thread: Lattice Points

1. ## 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.

2. Originally Posted by EinStone
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.