| Home  | About ScienceAsia  | Publication charge  | Advertise with us  | Subscription for printed version  | Contact us  
Editorial Board
Journal Policy
Instructions for Authors
Online submission
Author Login
Reviewer Login
Volume 49 Number 1
Volume 48 Number 6
Volume 48 Number 5
Volume 48 Number 4
Volume 48 Number 3
Volume 48 Number 2
Earlier issues
Volume 43 Number 5 Volume 43 Number 6

previous article next article

Research articles

ScienceAsia 43 (2017): 383-386 |doi: 10.2306/scienceasia1513-1874.2017.43.383

On some Diophantine equations over complex quadratic number fields

Malinee˙Chaiyaa, Somjate˙Chaiyaa, Supawadee˙Prugsapitakb,*

ABSTRACT:     In this paper, we establish a necessary and sufficient condition for two algebraic integers in complex quadratic number fields to be consecutive terms of generalized Fibonacci numbers. We use this result to obtain all solutions of the Diophantine equation x2axy+by2=c over Gaussian integers, where b and c are units in ℤ[i] and a∈ℤ[i] with |a|2≥10.

Download PDF

128 Downloads 1358 Views

a Department˙of˙Mathematics, Faculty˙of˙Science, Silpakorn˙University, Nakhon˙Pathom˙73000˙Thailand
b Algebra˙and˙Applications˙Research˙Unit, Department˙of˙Mathematics˙and˙Statistics, Faculty˙of˙Science, Prince˙of˙Songkla˙University, Songkhla˙90110˙Thailand

* Corresponding author, E-mail: supawadee.p@psu.ac.th

Received 15 Jan 2017, Accepted 31 Oct 2017