CONO-SUR 1993 Problem 5

Prove that there exists a succession $a_1, a_2, ... , a_k, ...$ , where each $a_i$ is a digit ( $a_i \in (0, 1, 2, 3, 4, 5, 6, 7, 8, 9)$ ) and $a_0=6$ , such that, for each positive integrer $n$ , the number $x_n=a_0+10a_1+100a_2+...+10^{n-1}a_{n-1}$ verify that $x_n^2-x_n$ is divisible by $10^n$ .