P3496
Factoring out $2$ from the expression $N !$, we can write
\begin{equation}
\begin{split}
N !
& = N (N - 1) (N - 2) \cdots 4 \cdot 3 \cdot 2 \cdot 1 \\
& = 2 \left( N (N - 1) (N - 2) \cdots 4 \cdot 3 \cdot 1 \right) \\
& = 2 k
\end{split}
\end{equation}
for $k = N (N - 1) (N - 2) \cdots 4 \cdot 3 \cdot 1$. $\square$
