Rearrange and multiply

Number Theory Level pending

Let \(n\) be an odd integer greater than 1.

Let \(A(1)\), \(A(2)\) ... \(A(n)\) be a rearrangement of the set {\(1\), \(2\), .... \(n\)}

Consider the product \((A(1) - 1) \times (A(2) - 2) \times ... (A(n)-n)\)

This product is...

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