# Modularity and Recursive Sequences

The sequence $$a_n$$ is defined by

$\large \begin{cases} a_0=3 \\ a_{n+1}-a_n=n(a_n-1) & \text{for } n \ge 0 \end{cases}$

Find all positive integers $$m$$ such that $$\gcd(m,a_n)=1$$ for all $$n \geq 0$$. What can the solution set for $$m$$ be best described as?

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