ON THE EQUATION y2 = x6 + k

被引：1

作者：

Nguyen Xuan Tho ^{[1
]}

机构：

[1] Hanoi Univ Sci & Technol, Sch Appl Math & Informat, Hanoi, Vietnam

来源：

ROCKY MOUNTAIN JOURNAL OF MATHEMATICS | 2020年 / 50卷 / 06期

关键词：

rational points; elliptic curve Chabauty; Diophantine equations;

D O I：

10.1216/rmj.2020.50.2167

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We find all rational solutions to the equation y(2) = x(6) + k, where k = -39 or k = -47. These are the two unsolved cases for k in the range vertical bar k vertical bar <= 50. Our method is elementary and can be applied to other situations to find all rational points on certain curves of genus 2.

引用

页码：2167 / 2178

页数：12

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