A number theory problem by Christopher Boo

For any positive integer \(n\), the following is true:

\(n\) is divisible by \(1.\)
\(n(n+1)\) is divisible by \(1\times 2.\)
\(n(n+1)(n+2)\) is divisible by \(1\times 2\times 3.\)

Is it true that \(n(n+1)(n+2)(n+3)\) must be divisible by \(1\times 2 \times 3\times 4?\)

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