POTW #15 - April 15, 2024
Contributed by: sawbez
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Difficulty: 10
This problem is tagged with potw, potw2024.
MCR Problem of the Week, April 15, 2024 Edition
The value of the product
$$
\prod_{n=1}^{2047} (n \hspace{-0em} \sqrt[23]{2})(n!){(n + 1)}^{n - 2047}
$$
can be expressed in the form $a! \times 2^b$ for some integers $a$ and $b$,
where $a$ is maximized. Find $a+b$.
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