Let S be the set of numbers of the form
\(n(n + 1)(n + 2)(n + 3)(n + 4),\)
where n is any positive integer. The first few terms of S are
\begin{align*}
1 \cdot 2 \cdot 3 \cdot 4 \cdot 5 &= 120, \\
2 \cdot 3 \cdot 4 \cdot 5 \cdot 6 &= 720, \\
3 \cdot 4 \cdot 5 \cdot 6 \cdot 7 &= 2520,
\end{align*}
and so on. What is the GCD of the elements of S?

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It says 6 is wrong.

You are right for your sequence.

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