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Values of coefficients of cyclotomic polynomials. (English) Zbl 1213.11059

Summary: Let \(a(k,n)\) be the \(k\)-th coefficient of the \(n\)-th cyclotomic polynomials. In 1987 [Proc. Japan Acad., Ser. A 63, 279–280 (1987; Zbl 0641.10008)], J. Suzuki proved that \(\{a(k,n)\mid n,\,k\in \mathbb N\}=\mathbb Z\). In this paper, we improve this result and prove that for any prime \(p\) and any integer \(l\geq 1\), we have \(\{a(k,p^ln)\mid n,\,k\in \mathbb N\} = \mathbb Z\).
Part II, cf. the authors and P. Moree, Discrete Math. 309, No. 6, 1720–1723 (2009; Zbl 1221.11067)

MSC:

11C08 Polynomials in number theory
11B83 Special sequences and polynomials
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References:

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[6] Suzuki, J., On coefficients of cyclotomic polynomials, Proc. Japan Acad. Ser. A Math. Sci., 63, 279-280 (1987) · Zbl 0641.10008
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