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Omni-MATH / Let ω₁,ω₂,…,ω₁₀₀ be the roots of (x¹⁰¹−1)/(x−1) (in some order). Consider the set S={ω₁¹,ω₂²,ω₃³,…,ω₁₀₀¹⁰⁰}. Let M be the maximum possible number of unique values in S, and let N b…

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problem

Let ω1,ω2,…,ω100\omega_{1}, \omega_{2}, \ldots, \omega_{100} be the roots of x101−1x−1\frac{x^{101}-1}{x-1} (in some order). Consider the set S={ω11,ω22,ω33,…,ω100100}S=\left\{\omega_{1}^{1}, \omega_{2}^{2}, \omega_{3}^{3}, \ldots, \omega_{100}^{100}\right\}. Let MM be the maximum possible number of unique values in SS, and let NN be the minimum possible number of unique values in SS. Find M−NM-N.
Plain-text mathematical notation (without MathML)
Let ω₁,ω₂,…,ω₁₀₀ be the roots of (x¹⁰¹−1)/(x−1) (in some order). Consider the set S={ω₁¹,ω₂²,ω₃³,…,ω₁₀₀¹⁰⁰}. 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.
Original LaTeX notation
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 $M-N$.

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Source and history

task_id
8842116b-8aa6-5b53-9e81-5b4480d2d81f
task_key
test--8842116b-8aa6-5b53-9e81-5b4480d2d81f
task_revision_id
1
config / split
/ test

Official source

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