30Edit: In the question α is e2πi/11.
Q. If α =e 2π/11 and f(x)=5+\sum_{k=1}^{60}{A_{k}x^{k}}, then find the value of \frac{1}{11}\sum_{r=0}^{10}{f(\alpha ^{r}x}).
Note: Integer type!
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2 Answers
1\alpha =e^{i\frac{2\pi}{7}} \\ f(x)=5+A_1x+A_2x^2+\cdots+A_{60}x^{60} \\ f(\alpha x)=5+A_1x\alpha+A_2x^2\alpha^2+\cdots \\ . \\.\\ .\\ f(\alpha^{10} x)=5+A_1x\alpha^{10}+\cdots \\ \sum_{r=0}^{10}f(\alpha^r x)=10(5+A_{11}x^{11} +A_{22}x^{22}+A_{33}x^{33}+A_{44}x^{44}+A_{55}x^{55})
this is what i can think of