Communications of the Korean Mathematical Society (대한수학회논문집)

Korean Mathematical Society (대한수학회)
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THE MINIMAL POLYNOMIAL OF cos(2π/n)

  • Gurtas, Yusuf Z. (Department of Mathematics and Computer Sciences Queensborough Community College)
  • Received : 2015.11.05
  • Published : 2016.10.31
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Abstract

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.

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References

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