TH-TMO 2010 Problem 8

Define the modulo $2553$ distance $d(x, y)$ between two integers $x, y$ to be the smallest nonnegative integer $d$ equivalent to either $x - y$ or $y - x$ modulo $2553$ . Show that, given a set S of integers such that $|S| \ge 70$ , there must be $m, n \in S$ with $d(m, n) \le 36$ .