Question 70
Let $a$ be a positive integer and $a \gt 1$. Prove that, for every positive integer $n$, the number
$$
n(2n + 1)(3n + 1)\dots(an + 1)
$$
is divisible by all prime numbers smaller than $a$.
$$
n(2n + 1)(3n + 1)\dots(an + 1)
$$
is divisible by all prime numbers smaller than $a$.