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 $\displaystyle (m,n)$, where *m* and *n* are integers.

A point $\displaystyle (m,n) \in \mathbb{Z}^2$ is called $\displaystyle invisible$ if the straight line segment from $\displaystyle (0,0)$ to $\displaystyle (m,n)$ goes through some other integer lattice point.

Show that for every $\displaystyle M > 0$ there exists a square in $\displaystyle \mathbb{Z}^2$ of side length M, so that all its lattice points are invisible.