If \( (1+a x)^{n}=1+8 x+24 x^{2}+\ldots, n \in \mathbf{N} \), then ...

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If \( (1+a x)^{n}=1+8 x+24 x^{2}+\ldots, n \in \mathbf{N} \), then find the values of \( a \) and \( n \).
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