Question 108
For a positive integer $r \ge 2$ each positive integer is coloured into one of $r$ colours. Suppose that for each integer number $n$ and each pair $(a, b)$ of two colours $a$ and $b$ the difference between the number of divisors of $n$ coloured $a$ and the number of divisors of $n$ coloured $b$ is at most $1$. Find all possible values of $r$.