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Winter 2003 Homogeneous Polynomials and the Minimal Polynomial of COS $(2\pi / n)$
David Surowski, Paul McCombs
Missouri J. Math. Sci. 15(1): 4-14 (Winter 2003). DOI: 10.35834/2003/1501014

Abstract

It is well known that if $\Phi _n (x)$ is the $n$th cyclotomic polynomial, then there is a factorization $x^n - 1 = \prod \Phi _d (x)$, where the product is taken over the divisors $d$ of $n$. Thus, one can obtain, by Möbius inversion, a product formula for each $\Phi _n (x)$ in terms of the various factors $x^d - 1$. The purpose of this note is two-fold. First, we show that the above factorization implies a similar factorization for the minimal polynomials of the algebraic numbers $\cos (2\pi / n)$, where $n$ is a positive integer. Secondly, we give an explicit formula for the minimal polynomials of $\cos (2\pi / p)$, where $p$ is prime.

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David Surowski. Paul McCombs. "Homogeneous Polynomials and the Minimal Polynomial of COS $(2\pi / n)$." Missouri J. Math. Sci. 15 (1) 4 - 14, Winter 2003. https://doi.org/10.35834/2003/1501014

Information

Published: Winter 2003
First available in Project Euclid: 31 August 2019

zbMATH: 1039.00506
MathSciNet: MR1959063
Digital Object Identifier: 10.35834/2003/1501014

Rights: Copyright © 2003 Central Missouri State University, Department of Mathematics and Computer Science

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Vol.15 • No. 1 • Winter 2003
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