Question 176
Given a positive integer $n$, let $D$ denote the set of all positive divisors of $n$. Let $A$ and $B$ be subsets of $D$ satisfying: for any $a \in A$ and $b \in B$, we have $a \nmid b$ and $b \nmid a$. Prove that
$$
\sqrt{|A|} + \sqrt{|B|} \le \sqrt{|D|}.
$$
$$
\sqrt{|A|} + \sqrt{|B|} \le \sqrt{|D|}.
$$