纺织高校基础科学学报2018，Vol.31Issue(1)：31-34,4.DOI:10.13338/j.issn.1006-8341.2018.01.006
关于不定方程x3-1=229y2
On the Diophantine equation x3-1=229y2
摘要
Abstract
Let D be a prime with D≡1(mod6).The solution of the Diophantine equation x3-1=Dy2 is one of the unsolved topics in number theory.The situation in the case of D=229 was studied by using some properties of the basic solutions to Pell equation,congruence and recur-rent sequence,it is proved that the Diophantine equation x3-1=229y2has only integer solu-tion(x,y)=(1,0).关键词
不定方程/整数解/递归数列/同余式Key words
Diophantine equation/integer solution/recurrent sequence/congruence分类
数理科学引用本文复制引用
杨晓柳,牟全武..关于不定方程x3-1=229y2[J].纺织高校基础科学学报,2018,31(1):31-34,4.基金项目
陕西省教育厅自然科学专项研究项目(17JK0341) （17JK0341）
