A subset $A$ of the natural numbers $\mathbb{N}=\{0,1,2, \ldots\}$ is called good if every integer $n>0$ has at most one prime divisor $p$ such that $n-p \in A$. (a) Show that the set $S=\{0,1,4,9, \ldots\}$ of perfect squares is good. (b) Find an infinite good set disjoint from $S$. (Two sets are disjoint if they have no common elements.)