PELL'S EQUATIONS IN GAUSSIAN INTEGERS

被引：0
|
作者：
Kharbuki, Algracia [1 ]
Singh, Madan Mohan [2 ]
机构：
[1] North Eastern Hill Univ, Dept Math, Shillong, Meghalaya, India
[2] North Eastern Hill Univ, Dept Basic Sci & Social Sci, Shillong, Meghalaya, India
来源：
JP JOURNAL OF ALGEBRA NUMBER THEORY AND APPLICATIONS | 2019年 / 42卷 / 01期
关键词：
complex continued fraction; Hurwitz continued fraction; recurrence relation; Pell's equation; Gaussian integers;
D O I：
10.17654/NT042010015
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
From Hurwitz's approach of complex continued fractions, we build a complex theory of the Pell's equation. In this paper, we study the complex theory of the Pell's equation, x(2) - Dy-2 = 2, that is, finding its solutions in Gaussian integers, using Hurwitz complex continued fraction, hence, generalizing it to the Pell's equation x(2) - Dy-2 = 2(n) and in the process we also develop some interesting properties.
引用
收藏
页码：15 / 32
页数：18
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