It is known that $a_1, a_2,...a_{108}$ are $108$ different positive integers not exceeding $2015$. Prove that there is a positive integer $k$ such that there are at least four different pairs $(i, j) $satisfying $a_i-a_j =k$.
Source: China Northern MO 2015 grade 11 p4 CNMO
Tags: combinatorics, number theory
It is known that $a_1, a_2,...a_{108}$ are $108$ different positive integers not exceeding $2015$. Prove that there is a positive integer $k$ such that there are at least four different pairs $(i, j) $satisfying $a_i-a_j =k$.