Question 51
Is there a positive integer $k$ such that
$$
(\cdots((4 \underbrace{!}_{k}) !) ! \cdots) !\gt (\cdots((3 \underbrace{!}_{k+1}) !) ! \cdots) ! ?
$$
$$
(\cdots((4 \underbrace{!}_{k}) !) ! \cdots) !\gt (\cdots((3 \underbrace{!}_{k+1}) !) ! \cdots) ! ?
$$