IJPAM: Volume 18, No. 4 (2005)

DEFINING A GROUP OPERATION ON THE SET
OF SOLUTIONS OF A PARAMETRISED
QUADRATIC DIOPHANTINE EQUATION

Kenneth K. Nwabueze$^1$, Omar Kihel$^2$, Ajai Choudhry$^3$
$^1$Department of Mathematics
University of Brunei
Jaban Tinguka Link
Bander Seno Bgawan, Darussalam, BE 1210, BRUNEI
$^2$Department of Mathematics
Brock University
St. Catharines, Ontario, L2S 3A1, CANADA
e-mail: okihel@brocku.ca
$^3$High Commission of India
P.O. Box 439, M.P.C., Airport Lama
Berakas, BB 3577, BRUNEI
e-mail: ajaic203@yahoo.com


Abstract.Using basic elementary geometric ideas, a binary operation defining an algebraic group induced by the set of all integral solutions to the diophantine equation of the form $ax^{2}
+ by^{2} = az^{2}$ is exhibited.

Received: November 29, 2004

AMS Subject Classification: 11D09, 20D15

Key Words and Phrases: diophantine equation, group, elementary geometry

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2005
Volume: 18
Issue: 4