| 郑惠,杨仕椿,袁平之.一些多项式xn±cxn−1±d的不可约性研究[J].数学年刊A辑,2026,(1):77~84 |
| 一些多项式xn±cxn−1±d的不可约性研究 |
| On the Irreducibility for Polynomial xn±cxn−1±d |
| Received:May 29, 2025 Revised:February 11, 2026 |
| DOI：10.16205/j.cnki.cama.2026.0007 |
| 中文关键词: 不可约性 有理数域 整系数多项式 三项式 |
| 英文关键词:Irreducibility Field of rational numbers Polynomial with integral coefficients Trinomials |
| 基金项目:国家自然科学基金(No.12361001, No.12571003);阿坝师范学院校级课题(No.AS-PYYB2023-08) |
| Author Name | Affiliation | | ZHENG Hui | School of Mathematics, Aba Teacher's College, Wenchan 623002, Sichuan, China | | YANG Shichun | School of Mathematics, Aba Teacher's College, Wenchan 623002, Sichuan, China | | YUAN Pingzhi | School of Mathematics Science, South China Normal University, Guangzhou 510631, China |
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| 中文摘要: |
| 设n, c, d为正整数, 满足n?2, 且ε1, ε2∈{?1,1}. 利用Rouché定理以及整系数多项式的牛顿多边形关于素数p的线段向量系统的结论, 讨论了三项整系数多项式xn±cxn?1±d在有理数域Q上的不可约性. 首先, 研究了多项式f(x)=xn+ε12r?1xn?1+ε22r在有理数域Q上的不可约性, 其中r为正整数. 其次, 研究了多项式g(x)=xn+4ε1xn?1+9ε2, xn+2ε1xn?1+3ε2在Q上的不可约性. |
| 英文摘要: |
| Let n, c, d be positive integers, and n?2, ε1, ε2∈{?1,1}. Using Rouché's theorem and the result on the segment vector system of the Newton polygon of an integral coefficient polynomial with respect to prime p, the authors study the irreducibility for the polynomial xn±cxn?1±d∈Z[x]. First, the authors study the irreducibility for the polynomial f(x)=xn+ε12r?1xn?1+ε22r, r∈N+. Second, the irreducibility of g(x)=xn+4ε1xn?1+9ε2, xn+2ε1xn?1+3ε2 is studied. |
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