On a conjecture on Pythagorean numbers
type: Item
instance of: scholarly article
title: On a conjecture on Pythagorean numbers
zbMATH Open document ID: 0796.11009
author: Kei Takakuwa
author: You Asaeda
published in: Proceedings of the Japan Academy. Series A
publication date: 1994-09-29T00:00:00Z
review text: L. Jésmanowicz conjectured that if \(u\), \(v\), \(w\) are Pythagorean numbers, then the diophantine equation on \(\ell,m,n\in\mathbb{N}\) \[ u^ \ell+ v^ m= w^ n \] has the unique solution \((\ell,m,n)= (2,2,2)\). In this paper, the authors prove this conjecture in some special cases.
Mathematics Subject Classification ID: 11D09
zbMATH DE Number: 549026
zbMATH Keywords: quadratic diophantine equation
zbMATH Keywords: Pythagorean numbers
Wikidata QID: Q114023246
MaRDI profile type: Publication
full work available at URL: pjaa.69.252
OpenAlex ID: W4240210767
cites work: Q3239359
cites work: The Diophantine equation $x^2 + q^m =p^n$
DOI: 10.3792/PJAA.69.252
reviewed by: Ke Zhao
description: scientific article; zbMATH DE number 549026