# 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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