Product of Totatives-I

Let \(\mathbb P\) be the product of all possible positive integers \(a\leq1000\) such that \(\gcd(a,1000)=1\).

Enter the remainder when \(\mathbb P\) is divided by 1000.

\(\)
Notation: \(\gcd(\cdot) \) denotes the greatest common divisor function.

Bonus: Generalize this for any positive integer \(n\) replacing 1000.

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