Question 64
Determine all possible positive integers $m$ and $n$, that satisfy the following:
$$
(m+n)! = 2m! \cdot n!
$$
where $k!$ denotes the product $1 \cdot 2 \cdot \dots \cdot k$, where $k$ is a positive integer.
$$
(m+n)! = 2m! \cdot n!
$$
where $k!$ denotes the product $1 \cdot 2 \cdot \dots \cdot k$, where $k$ is a positive integer.