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

Abstract

We show that the values of the minimal polynomials ${\varphi }_n(x)$ 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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