Question 71
Denote $S$ as the set of prime divisors of all integers of the form $2^{n^{2}+1}-3^{n}$, $n \in \mathbb{Z}^{+}$. Prove that $S$ and $\mathscr{P} \backslash S$ both contain infinitely many elements ($\mathscr{P}$ is the set of prime numbers).