A SYSTEM OF RELATIVE PELLIAN EQUATIONS AND A RELATED FAMILY OF RELATIVE THUE EQUATIONS-Reference-Cited by-同舟云学术

A SYSTEM OF RELATIVE PELLIAN EQUATIONS AND A RELATED FAMILY OF RELATIVE THUE EQUATIONS

Published:2006-12 Issue:04 Volume:02 Page:569-590
ISSN:1793-0421
Container-title:International Journal of Number Theory
language:en
Short-container-title:Int. J. Number Theory

Author:

JADRIJEVIĆ BORKA¹,ZIEGLER VOLKER²

Affiliation:

1. FESB, University of Split, Rujera Boškovića bb, 21000 Split, Croatia

2. Institut für Mathematik A, Technische Universität Graz, Steyrergasse 30, A-8010 Graz, Austria

Abstract

In this paper we consider the family of systems (2c + 1)U2 - 2cV2 = μ and (c - 2)U2 - cZ2 = -2μ of relative Pellian equations, where the parameter c and the root of unity μ are integers in the same imaginary quadratic number field [Formula: see text]. We show that for |c| ≥ 3 only certain values of μ yield solutions of this system, and solve the system completely for |c| ≥ 1544686. Furthermore we will consider the related relative Thue equation [Formula: see text] and solve it by the method of Tzanakis under the same assumptions.

Publisher

World Scientific Pub Co Pte Lt

Subject

Algebra and Number Theory

Link

https://www.worldscientific.com/doi/pdf/10.1142/S1793042106000735

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