MathDB

Let

\{\omega_1,\omega_2,\cdots,\omega_{100}\}

be the roots of

\frac{x^{101}-1}{x-1}

(in some order). Consider the set

S=\{\omega_1^1,\omega_2^2,\omega_3^3,\cdots,\omega_{100}^{100}\}.

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.

Problem Statement