Disregard the Book!

Algebra Level pending

Suppose \(n\) is a real positive Integer such that:

\[\frac{(n^{2})!}{(n-1)!} = \frac{(n^{2} -1)!}{(n-2)!} .\]

Find \(n^{8} - \dfrac{1}{n^{8}}\).

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