BY-MO 2004 Problem 4

For a positive integer $A = \overline{a_n ...a_1a_0}$ with nonzero digits which are not all the same ( $n \ge 0$ ), the numbers $A_k = \overline{a_{n-k}...a_1a_0a_n ...a_{n-k+1}}$ are obtained for $k = 1,2,...,n$ by cyclic permutations of its digits. Find all $A$ for which each of the $A_k$ is divisible by $A$ .