Some new results on the negative polynomial Pell's equation

被引：0

作者：

Anitha, K. ^{[1
]}

Fathima, I. Mumtaj ^{[2
]}

Vijayalakshmi, A. R. ^{[3
]}

机构：

[1] SRM IST Ramapuram, Dept Math, Chennai 600089, India

[2] Anna Univ, Sri Venkateswara Coll Engn, Dept Math, Chennai 602117, India

[3] Sri Venkateswara Coll Engn, Dept Math, Chennai 602117, India

来源：

NOTES ON NUMBER THEORY AND DISCRETE MATHEMATICS | 2024年 / 30卷 / 02期

关键词：

Pell's equation; Polynomial Pell's equation; Gaussian integers; ABC conjecture for polynomials; IDENTITIES;

D O I：

10.7546/nntdm.2024.30.2.223-235

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We consider the negative polynomial Pell's equation P 2 ( X ) - D ( X ) Q 2 ( X ) = - 1 , where D ( X ) is an element of Z [ X ] be some fixed, monic, square -free, even degree polynomials. In this paper, we investigate the existence of polynomial solutions P ( X ), Q ( X ) with integer coefficients.

引用

页码：223 / 235

页数：13

共 28 条

[1] The Seidel, Stern, Stolz and Van Vleck Theorems on continued fractions [J].