Question 76
Let $c$ be a positive integer and let $\{a_{n}\}_{n=1}^{\infty}$ be a sequence of positive integers such that $a_{n} \lt a_{n+1} \lt a_{n} + c$ for every $n \geq 1$. The terms of the sequence are written one after another and in this way one obtains an infinite sequence of digits. Prove that for every positive integer $m$ there exists a positive integer $k$ such that the number formed by the first $k$ digits of the above sequence is divisible by $m$.