Question 151
Determine whether there exists a finite set $S$ of prime numbers such that, for every integer $n \ge 2$, the number
$$
2^2 + 3^2 + \dots + n^2
$$
is divisible by some prime number $p \in S$.
$$
2^2 + 3^2 + \dots + n^2
$$
is divisible by some prime number $p \in S$.