Mordell’s equation: a classical approach

Q1 Mathematics Lms Journal of Computation and Mathematics Pub Date : 2013-11-27 DOI:10.1112/S1461157015000182

M. Bennett, Amir Ghadermarzi

引用次数: 19

Abstract

We solve the Diophantine equation $Y^{2}=X^{3}+k$ for all nonzero integers $k$ with $|k|\leqslant 10^{7}$ . Our approach uses a classical connection between these equations and cubic Thue equations. The latter can be treated algorithmically via lower bounds for linear forms in logarithms in conjunction with lattice-basis reduction.

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莫德尔方程:经典方法

我们用$|k|\leqslant 10^{7}$求解所有非零整数$k$的丢番图方程$Y^{2}=X^{3}+k$。我们的方法使用了这些方程和三次Thue方程之间的经典联系。后者可以通过结合格基约简的对数线性形式的下界算法处理。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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P. Nomikou, D. Evangelidis, D. Papanikolaou, D. Lampridou, Dimitris Litsas, Giannis Tsaparas, Ilias Koliopanos

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P. Nomikou, D. Evangelidis, D. Papanikolaou, D. Lampridou, Dimitris Litsas, Yannis Tsaparas, Ilias Koliopanos, Maria Petroulia

来源期刊

Lms Journal of Computation and Mathematics MATHEMATICS, APPLIED-MATHEMATICS

CiteScore

2.60

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： LMS Journal of Computation and Mathematics has ceased publication. Its final volume is Volume 20 (2017). LMS Journal of Computation and Mathematics is an electronic-only resource that comprises papers on the computational aspects of mathematics, mathematical aspects of computation, and papers in mathematics which benefit from having been published electronically. The journal is refereed to the same high standard as the established LMS journals, and carries a commitment from the LMS to keep it archived into the indefinite future. Access is free until further notice.