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arxiv: 0708.1423 · v1 · submitted 2007-08-10 · 🧮 math.NT

A property of cyclotomic polynomials

classification 🧮 math.NT
keywords polynomialscyclotomicdeterminegivenintegerminimalnaturalnumber
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Given two cyclotomic polynomials $\Phi_n(x)$ and $\Phi_m(x)$, $n\not= m$, we determine the minimal natural number k such that we can write $$k=a(x)\Phi_n (x)+b(x)\Phi_m(x),$$ with a(x) and b(x) integer polynomials.

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