On a conjecture on Pythagorean numbers. II
type: Item
instance of: scholarly article
title: On a conjecture on Pythagorean numbers. II
zbMATH Open document ID: 0796.11010
author: Kei Takakuwa
author: You Asaeda
published in: Proceedings of the Japan Academy. Series A
publication date: 1994-05-03T00:00:00Z
review text: In the paper reviewed above, the authors considered the following diophantine equation on \(\ell,m,n\in\mathbb{N}\), \[ (4a^ 2- y^ 2)^ \ell+ (4 ay)^ m= (4 a^ 2+ y^ 2)^ n, \tag{1} \] where \(a,y\in\mathbb{N}\) with \((a,y)=1\), \(2a>y\), \(y\equiv 3\pmod 4\). In this paper, they consider the case \(y=3\). They prove that in some cases, the only solution of (1) is \((\ell,m,n)= (2,2,2)\).
Mathematics Subject Classification ID: 11D09
zbMATH DE Number: 549034
zbMATH Keywords: Pythagorean numbers
zbMATH Keywords: quadratic diophantine equation
MaRDI profile type: Publication
full work available at URL: pjaa.69.287
OpenAlex ID: W4230261363
Wikidata QID: Q114023245
cites work: On a conjecture on Pythagorean numbers
cites work: Q3765869
DOI: 10.3792/PJAA.69.287
reviewed by: Ke Zhao
description: scientific article; zbMATH DE number 549034