Question 17
Let $\omega_{1}, \omega_{2}, \ldots, \omega_{100}$ be the roots of $\frac{x^{101}-1}{x-1}$ (in some order). Consider the set
$$
S=\left\{\omega_{1}^{1}, \omega_{2}^{2}, \omega_{3}^{3}, \ldots, \omega_{100}^{100}\right\}
$$
Let $M$ be the maximum possible number of unique values in $S$, and let $N$ be the minimum possible number of unique values in $S$. Find $M-N$.
$$
S=\left\{\omega_{1}^{1}, \omega_{2}^{2}, \omega_{3}^{3}, \ldots, \omega_{100}^{100}\right\}
$$
Let $M$ be the maximum possible number of unique values in $S$, and let $N$ be the minimum possible number of unique values in $S$. Find $M-N$.