Question 38
Let $n$ be a positive integer, and let $A$ and $B$ be coprime positive integers such that
$$
\left(\frac{n(n+1)}{2}\right)! \cdot \prod_{k=1}^{n} \frac{k!}{(2k)!} = \frac{B}{A}.
$$
Prove that $A$ is a power of 2.
$$
\left(\frac{n(n+1)}{2}\right)! \cdot \prod_{k=1}^{n} \frac{k!}{(2k)!} = \frac{B}{A}.
$$
Prove that $A$ is a power of 2.