SOLUTIONS OF NEGATIVE PELL EQUATION INVOLVING TWIN PRIME

被引：4

作者：

Kannan, J. ^{[1
]}

Somanath, Manju ^{[2
]}

Raja, K. ^{[2
]}

机构：

[1] Ayya Nadar Janaki Ammal Coll, Dept Math, Sivakasi 626124, India

[2] Natl Coll, Dept Math, Tiruchirappalli 620001, India

来源：

JP JOURNAL OF ALGEBRA NUMBER THEORY AND APPLICATIONS | 2018年 / 40卷 / 05期

关键词：

Diophantine equation; Pell's equation; Brahma Gupta lemma;

D O I：

10.17654/NT040050869

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Let d not equal 1 be a positive non-square integer and N be any fixed positive integer. Then the equation x(2) - dy(2) = +/- N is known as Pell's equation named after the famous mathematician John Pell. In this paper, we fix d and N to be twin prime 41 and 43 and search for non-trivial integer solution to the equation x(2) = 41y(2) - 43(t), t is an element of N for the different choices of t given by (i) t = 1, (ii) t = 3, (iii) t = 5, (iv) t = 2k, and (v) t = 2k + 5, for all k is an element of N. Further, recurrence relation on the solutions are obtained.

引用

页码：869 / 874

页数：6