Question 65
Let $n \ge 3$ be a given integer, and $S \ge 1$ be a multiple of $10^n - 3$. Suppose that the decimal expansion of $S$ has $m$ digits and $2n - 1 \gt m \gt n$. Show that $S$ has at least 3 different digits.
(Bayarmagnai Gombodorj)
(Bayarmagnai Gombodorj)