Problem

Source: Switzerland - Swiss TST 2003 p9

Tags: number theory, combinatorics, divides



Given integers $0 < a_1 < a_2 <... < a_{101} < 5050$, prove that one can always choose for different numbers $a_k,a_l,a_m,a_n$ such that $5050 | a_k +a_l -a_m -a_n$