Question 97
A subset $A$ of the natural numbers $\mathbb{N}=\{0,1,2, \ldots\}$ is called good if every integer $n \gt 0$ 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.)
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.)