Find It Without Plugging Values

n!+1(n+1)!+1 \large n! + 1 \qquad \qquad (n+1)! + 1

If nn is a positive integer, find the greatest common divisor of the two numbers above.

Notation: !! denotes the factorial notation. For example, 8!=1×2×3××88! = 1\times2\times3\times\cdots\times8 .

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