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

页码：15 / 32

页数：18

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