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The nth cyclotomic polynomial is the minimal polynomial over \(\mathbb {Q}\) with root e2πi∕n, denoted Φn(q). We can write this polynomial as \(\varPhi _n(q) = \prod \limits _{ \substack {\omega ^n =1 , \omega ^k \neq 1 \text{ for } k<n}} (q- \omega )\). An important property to note is that we can write qn − 1 as a product of cyclotomic polynomials, \(\prod \limits _{d \mid n} \varPhi _d(q).\)
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Przytycki, J.H., Bakshi, R.P., Ibarra, D., Montoya-Vega, G., Weeks, D. (2024). Plucking Polynomial of Rooted Trees and Its Use in Knot Theory. In: Lectures in Knot Theory. Universitext. Springer, Cham. https://doi.org/10.1007/978-3-031-40044-5_10
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