ISL 2007 C5

In the Cartesian coordinate plane define the strip $S_{n}=\{(x, y) \mid n \leq x<n+1\}$ for every integer $n$. Assume that each strip $S_{n}$ is colored either red or blue, and let $a$ and $b$ be two distinct positive integers. Prove that there exists a rectangle with side lengths $a$ and $b$ such that its vertices have the same color. (Romania)