二次域Q(3^(1/2))的单位给出的两个递归数列中的三角数问题  

Problems of Triangular Numbers in Two Recurrent Sequences Arising in the Units of Quadratic Field Q(3^(1/2))

作　　者：罗明[1] 

机构地区：[1]四川大学数学学院

出　　处：《数学年刊（A辑）》2008年第2期283-290,共8页Chinese Annals of Mathematics

基　　金：重庆市教委科研课题基金(No．KJ050807)资助的项目．

摘　　要：对二次域Q(3^(1/2))中单位V_n+U_n 2^(1/2)=(2+3^(1/2))~n所给出的两个递归数列{V_n},{U_n}中的三角数问题进行研究,给出了完整的结果.作为应用,解决了与其相关的两个不定方程问题.This paper discusses the problems of triangular numbers in two recurrent sequences Vn and Un, which are arising in the units Vn＋ Un√3 = （2 ＋ √3）^n of quadratic field Q（√3）, and solves the problems completely and finds out all triangular numbers in Vn and Un. As applications, all integer solutions of two Diophantine equations involved are obtained.

关 键 词：二次域 单位 递归数列 三角数 不定方程 

分 类 号：O156[理学—数学]