CN-SMO 2008 Problem 4

Let $m, n$ be positive integers $(m, n>=2)$ . Given an $n$ -element set $A$ of integers $(A=\{a_1,a_2,\cdots ,a_n\})$ , for each pair of elements $a_i, a_j(j>i)$ , we make a difference by $a_j-a_i$ . All these $C^2_n$ differences form an ascending sequence called "derived sequence" of set $A$ . Let $\bar{A}$ denote the derived sequence of set $A$ . Let $\bar{A}(m)$ denote the number of terms divisible by $m$ in $\bar{A}$ . Prove that $\bar{A}(m)\ge \bar{B}(m)$ where $A=\{a_1,a_2,\cdots ,a_n\}$ and $B=\{1,2,\cdots ,n\}$ .