Question 76
Let $h \ge 3$ be an integer and $X$ the set of all positive integers that are greater than or equal to $2h$. Let $S$ be a nonempty subset of $X$ such that the following two conditions hold:
* if $a + b \in S$ with $a \ge h, b \ge h$, then $ab \in S$;
* if $ab \in S$ with $a \ge h, b \ge h$, then $a+b \in S$.
Prove that $S = X$.
* if $a + b \in S$ with $a \ge h, b \ge h$, then $ab \in S$;
* if $ab \in S$ with $a \ge h, b \ge h$, then $a+b \in S$.
Prove that $S = X$.