Some remarks about the minimal polynomials of $4{\sin ^2}\left( {\frac{\pi }{n}} \right)$

Johann Cigler

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arXiv · 2503.19422

Some remarks about the minimal polynomials of $4{\sin ^2}\left( {\frac{\pi }{n}} \right)$

Johann Cigler

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Abstract

We show that the values of the minimal polynomials ${\phi_n}(x)$ of $4{\sin ^2}\left( {\frac{\pi }{n}} \right)$ for $x \in \left\{ {0,1,2,3,4} \right\}$ are intimately related to the prime factorization of $n.$

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Johann Cigler. 2025-03-25. Some remarks about the minimal polynomials of $4{\sin ^2}\left( {\frac{\pi }{n}} \right)$. https://arxiv.org/abs/2503.19422

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