Products of consecutive integers and the Markoff equation
type: Item
instance of: scholarly article
title: Products of consecutive integers and the Markoff equation
zbMATH Open document ID: 0845.11012
DOI: 10.1007/BF01831145
author: Arthur Baragar
published in: Aequationes Mathematicae
publication date: 1996-05-09T00:00:00Z
full work available at URL: https://eudml.org/doc/137635
review text: \textit{S. Katayama} [Proc. Japan Acad., Ser. A 66, 305-306 (1990; Zbl 0755.11011)] described all integral solutions to the diophantine equation \(X(X+ 1) Y(Y+ 1)= Z(Z+ 1)\). The author clarifies the description by using a bijection studied by Mordell with \(x^2+ y^2+ z^2= 2xyz+ 5\). Also, it is shown that the number of positive integer solutions with \(Z\leq H\) to Katayama's equation is of order \(\sqrt H\), and, in general, the number of solutions to Mordell's equation \(x^2+ y^2+ z^2= axyz+ b\) with height less than \(H\) is counted.
Mathematics Subject Classification ID: 11D25
Mathematics Subject Classification ID: 11D72
Mathematics Subject Classification ID: 11D09
zbMATH DE Number: 856830
zbMATH Keywords: products of consecutive integers
zbMATH Keywords: Markoff equation
zbMATH Keywords: diophantine equation
zbMATH Keywords: Katayama's equation
zbMATH Keywords: number of solutions to Mordell's equation
reviewed by: Edward L. Cohen
MaRDI profile type: Publication
cites work: Q3241280
cites work: On products of consecutive integers
cites work: Q3977283
cites work: On the Integer Solutions of the Equation x 2 +y 2 +z 2 +2xyz = n
cites work: Q5582375
cites work: On the Number of Markoff Numbers Below a Given Bound
description: scientific article; zbMATH DE number 856830