| On the Family of Thue Equation ｜x^3 ＋ mx^2y-（ m ＋ 3）xy^2 ＋ y^3｜= k |
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| 引用本文： | XIA Jingbo CHEN Jianhua ZHANG Silan. On the Family of Thue Equation ｜x^3 ＋ mx^2y-（ m ＋ 3）xy^2 ＋ y^3｜= k[J]. 武汉大学学报:自然科学英文版, 2006, 11(3): 481-485. DOI: 10.1007/BF02836648 |
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| 作者姓名： | XIA Jingbo CHEN Jianhua ZHANG Silan |
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| 作者单位： | School of Mathematics and Statistics, Wuhan University, Wuhan 430072, Hubei, China |
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| 基金项目： | 国家高技术研究发展计划(863计划) |
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| 摘 要： | The family of cubic Thue equation which depend on two parameters ｜ x^3 ＋ mx^2 y-（m＋3） xy^2＋y^3｜=k is studied. Using rational approximation, we give a smaller upper bound of the solution of the equation, that is quite better than the present result. Moreover, we study two inequalities ｜ x^3 ＋ mx^2y-（m ＋ 3） xy^2＋y^3 ｜ =k≤2m＋3 and ｜x^3 ＋mx^2y- （m＋3）xy^2 ＋ y^3｜ = k≤ （2m＋3）^2 separately. Our result of upper bound make it easy to solve those inequalities by simple method of continuous fraction expansion.
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| 关 键 词： | 三次方程 不等式 连续分数展开 边界搜索 |
| 文章编号： | 1007-1202（2006）03-0481-05 |
| 收稿时间： | 2005-06-26 |
On the family of Thue equation|x 3+mx2y−(m+3)xy2+y3|=k |
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| Xia Jingbo,Chen Jianhua,Zhang Silan. On the family of Thue equation|x 3+mx2y−(m+3)xy2+y3|=k[J]. Wuhan University Journal of Natural Sciences, 2006, 11(3): 481-485. DOI: 10.1007/BF02836648 |
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| Authors: | Xia Jingbo Chen Jianhua Zhang Silan |
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| Affiliation: | (1) School of Mathematics and Statistics, Wuhan University, 430072 Wuhan, Hubei, China |
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| Abstract: | The family of cubic Thue equation which depend on two parameters|x 3+mx2y−(m+3)xy2+y3|=k is studied. Using rational approximation, we give a smaller upper bound of the solution of the equation, that is quite better than the present result. More over we study two inequalities|x 3+mx2y−(m+3)xy2+y3|=k≤2m+3 and|x 3+mx2y−(m+3)xy2+y3|=k≤(2m+3)2 separately. Our result of upper bound make it easy to solve those inequalities by simple method of continuous fraction expansion. Foundation item: Supported by the National Natural Science Foundation of China (2001AA141010) Biography: XIA Jingho(1979-), male, Ph. D. candidate, research direction: number theory and cryptography. |
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| Keywords: | parametric Thue equation Thue inequality continuous fraction expansion bound search |
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