If \( \mathrm{P}(n) \) is the statement " \( n(n+1)(n+2) \) is an i...

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If \( \mathrm{P}(n) \) is the statement " \( n(n+1)(n+2) \) is an integral multiple of \( 12 " \), prove that \( \mathrm{P}(3) \) and \( P(4) \) are true but \( P(5) \) is not true.
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