CONO-SUR 2016 Problem 1

Let $\overline{abcd}$ be one of the 9999 numbers $0001, 0002, 0003, \ldots, 9998, 9999$ . Let $\overline{abcd}$ be an special number if $ab-cd$ and $ab+cd$ are perfect squares, $ab-cd$ divides $ab+cd$ and also $ab+cd$ divides $abcd$ . For example 2016 is special. Find all the $\overline{abcd}$ special numbers.Note: If $\overline{abcd}=0206$ , then $ab=02$ and $cd=06$ .