THE MINIMAL POLYNOMIAL OF cos(2π/n)
Yusuf Z. Gürtaş · Communications of the Korean Mathematical Society · 2016
In this article we show a recursive method to compute the coefficients of the minimal polynomial of cos( $2{\pi}/n$ ) explicitly for $n{\geq}3$ . The recursion is not on n but on the coefficient index. Namely, for a given n, we show how to compute ei of the minimal polynomial ${\sum_{i=0}^{d}}(-1)^ie_ix^{d-i}$ for $i{\geq}2$ with initial data $e_0=1$ , $e_1={\mu}(n)/2$ , where ${\mu}(n)$ is the $M{\ddot{o}}bius$ function.