Product Over 13th Roots of Unity

2175ExpertPolynomialsComplex Numbers

AIME II · 2024 · Problem 13

Let $\omega\neq 1$ be a $13$th root of unity. Find the remainder when $$\prod_{k=0}^{12}(2-2\omega^k+\omega^{2k})$$ is divided by $1000$.

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2175ExpertPolynomialsComplex Numbers

AIME II · 2024 · Problem 13

Let $\omega\neq 1$ be a $13$th root of unity. Find the remainder when $$\prod_{k=0}^{12}(2-2\omega^k+\omega^{2k})$$ is divided by $1000$.

0 students attempted0% solvedRating 2175