Do there exist distinct non-zero digits $a, b$ and $c$ such that the two-digit number $\overline{ab}$ is divisible by $c$, the number $\overline{bc}$ is divisible by $a$ and $\overline{ca}$, is divisible by $b$?
Problem
Source: 2002 Estonia National Olympiad Final Round grade 9 p2
Tags: Digits, divisible, number theory