Bartłomiej Bzdęga, Andrés Herrera-Poyatos, Pieter Moree
Abstract
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The $n$th cyclotomic polynomial $\varPhi _n(x)$ is the minimal polynomial of an $n$th primitive root of unity. Hence $\varPhi _n(x)$ is trivially zero at primitive $n$th roots of unity. Using finite Fourier analysis we derive a formula for $\varPhi _n(x)$
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The $n$th cyclotomic polynomial $\varPhi _n(x)$ is the minimal polynomial of an $n$th primitive root of unity. Hence $\varPhi _n(x)$ is trivially zero at primitive $n$th roots of unity. Using finite Fourier analysis we derive a formula for $\varPhi _n(x)$
Key concepts: Root of unity, Cyclotomic polynomial, Mathematics, Primitive root modulo n, Polynomial, Pi, Zero (linguistics), Combinatorics