Consider the set $A=\{1,2,...,120\}$ and $M$ a subset of $A$ such that $|M|=30$.Prove that there are $5$ different subsets of $M$,each of them having two elements,such that the absolute value of the difference of the elements of each subset is the same.
Problem
Source: Danube Mathematical Competition,Juniors #2
Tags: combinatorics, number theory, absolute value