ILL 1986 Problem 55

Given an integer $n \geq 2$ , determine all $n$ -digit numbers $M_0 = \overline{a_1a_2 \cdots a_n} \ (a_i \neq 0, i = 1, 2, . . ., n)$ divisible by the numbers $M_1 = \overline{a_2a_3 \cdots a_na_1}$ , $M_2 = \overline{a_3a_4 \cdots a_na_1 a_2}$ , $\cdots$ , $M_{n-1} = \overline{a_na_1a_2 . . .a_{n-1}}.$