Let $a, m$ be two positive integers, $a \ne 10^k$, for all non-negative integers $k$ and $d_1, d_2, ... , d_m$ random decimal$^1$ digits with $d_1 > 0$. Prove that there exists some positive integer $n$ for which the representation in the decimal base of the number $a^n$ begins with the digits $d_1, d_2, ... , d_m$ in this order. $^1$ lesser or equal with $9$