Note on a paper of Kobayashi and Nakagawa (Q2731723)
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scientific article; zbMATH DE number 1626401
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Note on a paper of Kobayashi and Nakagawa |
scientific article; zbMATH DE number 1626401 |
Statements
23 January 2002
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solvable quintics
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Galois group
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Note on a paper of Kobayashi and Nakagawa (English)
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The authors look at the polynomial \(f(x)= x^5+ ax^3+ bx^2+ cx+d\in \mathbb{Z}[x]\) having Galois group \(\mathbb{Z}/5\mathbb{Z}\). They determine the set of primes \(q\) such that \(f(x)\equiv (x+r)^5\pmod q\) for some \(r\in \mathbb{Z}\); and they relate this to the algorithm of \textit{S. Kobayashi} and \textit{H. Nakagawa} [Math. Jap. 37, 883-886 (1992; Zbl 0767.12005)] for determining \(x^5+ax^3+bx^2+cx+d=0\).
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