On the diophantine equation \(x(x+ 1)= y(y+ 1)z^ 2\)
type: Item
instance of: scholarly article
title: On the diophantine equation \(x(x+ 1)= y(y+ 1)z^ 2\)
zbMATH Open document ID: 0861.11019
author: Kenji Kashihara
published in: Proceedings of the Japan Academy. Series A
publication date: 1996-10-22T00:00:00Z
review text: Let \(f\) be an arbitrary integer. \textit{I. I. Mihailov} [Gaz. Mat., Bucuresti, Ser. A 78, 28-30 (1973; Zbl 0255.10021)] proved that \((x,y,z) = (4f^2+4f, f,4f+2)\) is a solution to the equation \(x(x+1) = y(y+1) z^2\). In this paper, a complete solution is given.
Mathematics Subject Classification ID: 11D25
zbMATH DE Number: 938089
zbMATH Keywords: quartic diophantine equations
reviewed by: Edward L. Cohen
MaRDI profile type: Publication
full work available at URL: pjaa.72.91
OpenAlex ID: W2021195761
cites work: On products of consecutive integers
cites work: Q5582375
DOI: 10.3792/PJAA.72.91
description: scientific article; zbMATH DE number 938089