Question 93
Let $(a_n)$ be the integer sequence which is defined by $a_1 = 1$ and
$$
a_{n+1} = a_n^2 + n \cdot a_n, \forall n \ge 1.
$$
Let $S$ be the set of all primes $p$ such that there exists an index $i$ such that $p|a_i$. Prove that the set $S$ is an infinite set and it is not equal to the set of all primes.
$$
a_{n+1} = a_n^2 + n \cdot a_n, \forall n \ge 1.
$$
Let $S$ be the set of all primes $p$ such that there exists an index $i$ such that $p|a_i$. Prove that the set $S$ is an infinite set and it is not equal to the set of all primes.