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$\dfrac{n+1}{1},\ \dfrac{n+2}{2},\ \dfrac{n+3}{3},\ \dfrac{n+4}{4},\ \dfrac{n+5}{5}$

With $n=0$, all of the above numbers are integers (they all equal 1). What is the next positive integer $n$ such that all of the above numbers are integers?

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