Unit Root Inversion

And trying to figure out what it’s like moving on.

Summary

$$ [n \mid k] = \frac{1}{n} \sum_{i = 0}^{n - 1} \omega^{ik}_{n} $$

九个太阳

$$ \begin{aligned} &\sum_{i = 0}^{n} \binom{n}{i} \frac{1}{k} \sum_{j = 0}^{k - 1} \omega_{k}^{ij} \\ =&\frac{1}{k} \sum_{i = 0}^{n} \binom{n}{i} \sum_{j = 0}^{k - 1} (\omega_{k}^{j})^i \\ =&\frac{1}{k} \sum_{j = 0}^{k - 1} \sum_{i = 0}^{n} \binom{n}{i} (\omega_{k}^j)^i \\ =&\frac{1}{k} \sum_{j = 0}^{k - 1} (\omega_{k}^{j} + 1)^n \end{aligned} $$