# Looks simple, doesn't it?

**Number Theory**Level 3

\[\large \sum_{k=1}^{n}k!=a^{b}\]

Let \(a > 1, b > 1\) and \(n > 1\) be positive integers for which the summation above is fulfilled. Find the largest possible value of \((a+b+n)^{2}\).

\[\large \sum_{k=1}^{n}k!=a^{b}\]

Let \(a > 1, b > 1\) and \(n > 1\) be positive integers for which the summation above is fulfilled. Find the largest possible value of \((a+b+n)^{2}\).

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