Coefficients of cyclotomic polynomials

Details Coefficients of cyclotomic polynomials Coefficients of cyclotomic polynomials

2009-09-05

arxiv.org/abs/0909.0995v1

Mathematics

Number Theory

5pages

Scientific paper

Let $a(n, k)$ be the $k$-th coefficient of the $n$-th cyclotomic polynomial.
Recently, Ji, Li and Moree \cite{JLM09} proved that for any integer $m\ge1$,
$\{a(mn, k)| n, k\in\mathbb{N}\}=\mathbb{Z}$. In this paper, we improve this
result and prove that for any integers $s>t\ge0$,
$$\{a(ns+t, k)| n, k\in\mathbb{N}\}=\mathbb{Z}.$$

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