EXPLICIT COMPLETE SOLUTION IN INTEGERS OF A CLASS OF EQUATIONS (AX(2)-B)(AY(2)-B)=Z(2)-C

Authors
KASHIHARA K
Citation
K. Kashihara, EXPLICIT COMPLETE SOLUTION IN INTEGERS OF A CLASS OF EQUATIONS (AX(2)-B)(AY(2)-B)=Z(2)-C, Manuscripta mathematica, 80(4), 1993, pp. 373-392
Citations number
6
Categorie Soggetti
Mathematics, General",Mathematics
Journal title
Manuscripta mathematica → ACNP
ISSN journal
00252611
Volume
80
Issue
4
Year of publication
1993
Pages
373 - 392
Database
ISI
SICI code
0025-2611(1993)80:4<373:ECSIIO>2.0.ZU;2-5
Abstract
In this paper we will study the equation for arbitrary integers a not- equal 0, c and b = +/- 1, +/- 2 or +/- 4. When b = +/- 4, we suppose c is divisible by 4. The paper will provide one with a method for findi ng algorithmically all integral non-trivial solutions of the title equ ations, where an explicit unit of Q(square-root a2n2 - ab) plays an im portant role.