Question 87
The sequence $a_0, a_1, a_2, \dots$ of integers is defined by $a_0 = 3$ and
$$
a_{n+1} - a_n = n(a_n - 1)
$$
for all $n \ge 0$. Determine all integers $m \ge 2$ for which $\gcd(m, a_n) = 1$ for all $n \ge 0$.
$$
a_{n+1} - a_n = n(a_n - 1)
$$
for all $n \ge 0$. Determine all integers $m \ge 2$ for which $\gcd(m, a_n) = 1$ for all $n \ge 0$.