Question 24
We call an infinite set $S \subseteq \mathbb{N}$ *good* if for all pairwise distinct integers $a$, $b$, $c \in S$, all positive divisors of $\frac{a^c - b^c}{a - b}$ are in $S$. For all positive integers $n \gt 1$, prove that there exists a good set $S$ such that $n \notin S$.