| Integral Points on a Class of Elliptic Curve |
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| 作者姓名： | ZHU Huilin CHEN Jianhua~ School of Mathematics and Statistics Wuhan University Wuhan Hubei China |
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| 作者单位： | ZHU Huilin，CHEN Jianhua~ School of Mathematics and Statistics，Wuhan University，Wuhan 430072，Hubei，China |
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| 摘 要： | 0 IntroductionZasegairerch1]fodre sbcirgibientde gsreavle rpaolin tmse tohnocdsert waihnicehlli ppetircm citur ovnese btyogiving the upper bound of solution. Unfortunately,this upperbound was verylarge andsometi mes beyondthe range of com-puter searching.For a particular elliptic curvey2=x3-30x+133(1)he mentioned he can find all integral points and the largestpoint is (x,y) =(5 143 326 ,±11 664 498 677) by using Mas-ser and W櫣stholz bounds on elliptic logarithms .Although recent results on…
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| 关 键 词： | 丢番图方程 椭圆曲线 基本单位 代数数因式分解 整点 |
| 文章编号： | 1007-1202（2006）03-0477-04 |
| 收稿时间： | 2005-06-14 |
Integral points on a class of elliptic curve |
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| Zhu Huilin,Chen Jianhua.Integral Points on a Class of Elliptic Curve[J].Wuhan University Journal of Natural Sciences,2006,11(3):477-480. |
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| Authors: | Zhu Huilin Chen Jianhua |
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| Institution: | (1) School of Mathematics and Statistics, Wuhan University, 430072 Wuhan, Hubei, China |
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| Abstract: | We prove all integral points of the elliptic curvey
2=x
3−30x+133 are (x, y)=(−7, 0), (−3,±14), (2, ±9), (6,±13), (5 143 326,±11 664 498 677), by using the method of algebraic number theory andp-adic analysis. Furthermore, we develop a computation method to find all integral points on a class of elliptic curvey
2=(x+a)(x
2−ax+b),a,b∈Z,a
2<4b and find all integer solutions of hyperelliptic Diophantine equationDy
2=Ax
1+Bx
2+C,B
2<4AC.
Foundation item: Supported by the National Natural Science Foundation of China (2001AA141010)
Biography: ZHU Huilin(1980-), male, Ph. D. candidate, research direction: number theory and eryptography. |
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| Keywords: | Diophantine equation elliptic curve fundamental unit algebraic number factorization p-adic analysis method |
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