ID | 14079 |
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Sort Key | 1
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フルテキストURL | |
著者 |
Nogami, Yasuyuki
The Graduate School of Natural Science and Technology Okayama University
Kaken ID
publons
researchmap
Morikawa, Yoshitaka
The Graduate School of Natural Science and Technology Okayama University
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抄録 | In this paper, we first show the number of x's such that x(2) +u, u ∈ F(*)(p) , becomes a quadratic residue in F(p), and then this number is proven to be equal to (p+1)/2 if −u is a quadratic residue in Fp, which is a necessary fact for the following. With respect to the irreducible cubic polynomials over Fp in the form of x(3)+ax+b, we give a classification based on the trace of an element in F(p3) and based on whether or not the coefficient of x, i.e. the parameter a, is a quadratic residue in Fp. According
to this classification, we can know the minimal set of the irreducible cubic polynomials, from which all the irreducible cubic polynomials can be generated by using the following two variable transformations: x=x + i, x=j−1x, i, j ∈ Fp, j ≠ 0. Based on the classification and that necessary fact, we show the number of the irreducible cubic polynomials in the form of x(3)+ax+b, b ∈ F(p), where a is a certain fixed element in F(p).
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キーワード | Irreducible cubic polynomial
trace
quadratic residue
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出版物タイトル |
Memoirs of the Faculty of Engineering, Okayama University
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発行日 | 2007-01
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巻 | 41巻
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号 | 1号
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出版者 | Faculty of Engineering, Okayama University
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出版者(別表記) | 岡山大学工学部
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開始ページ | 1
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終了ページ | 10
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ISSN | 0475-0071
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NCID | AA10699856
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資料タイプ |
紀要論文
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OAI-PMH Set |
岡山大学
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言語 |
英語
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論文のバージョン | publisher
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NAID | |
Eprints Journal Name | mfe
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