Let $a$ and $d$ be positive integers. For any positive integer $n$, the number $a+nd$ contains a block of consecutive digits which constitute the number $n$. Prove that $d$ is a power of 10.
Source: ToT - 2001 Fall Senior A-Level #5
Tags: number theory unsolved, number theory
Let $a$ and $d$ be positive integers. For any positive integer $n$, the number $a+nd$ contains a block of consecutive digits which constitute the number $n$. Prove that $d$ is a power of 10.