# 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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