\[\overline{(n-1)(n-2)(n-3)(n-4)(n-5)}_n\] is divisible by \(n^2-1\) for all \(n \geq 6\)

**Clarification**: The subscript means number base \(n\). The line above the number means that \((n-1), (n-2), \ldots\) are digits of the number.

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