RU-ALLRUSSIAN 1976 Problem 4

$\mathrm{a_1}$ and $\mathrm{a_2}$ are positive integers less than 1000. Define $\mathrm{a_n = min\{|a_i - a_j|:0< i< j< n\}}$ . Show that $\mathrm{a_{21} = 0}$ .