If \( \alpha=e^{2 \pi i / 17} \) and \( f(x)=7+\sum_{K=1}^{100} A_{...

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If \( \alpha=e^{2 \pi i / 17} \) and \( f(x)=7+\sum_{K=1}^{100} A_{K} x^{K} \) then find the value of \( \frac{1}{17} \sum_{r=0}^{16} f\left(\alpha^{r} x\right) \)
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