高师理科学刊2026，Vol.46Issue(2)：6-8,13,4.DOI:10.3969/j.issn.1007-9831.2026.02.002
椭圆曲线y2=x3+x-10的整数点
Integer points of the elliptic curve y2=x3+x-10
摘要
Abstract
Based on the fundamental properties of the Pell equation,this paper employs elementary methods such as recursive sequences,congruence ideas,and quadratic residues to derive and prove that the elliptic curve y2=x3+x-10 have only the non-trivial solution(x,y)=(2,0).关键词
椭圆曲线/Pell方程/递推序列/整数解Key words
elliptic curve/Pell equation/recursive sequence/integer solution分类
数理科学引用本文复制引用
林丽娟,李双娥..椭圆曲线y2=x3+x-10的整数点[J].高师理科学刊,2026,46(2):6-8,13,4.基金项目
重庆市教育委员会科学技术研究项目(KJQN202204501) （KJQN202204501）
江西省教育厅科学技术研究项目(GJJ2509402) （GJJ2509402）
