On Jeśmanowicz' conjecture concerning Pythagorean numbers
type: Item
instance of: scholarly article
title: On Jeśmanowicz' conjecture concerning Pythagorean numbers
zbMATH Open document ID: 0876.11013
published in: Proceedings of the Japan Academy. Series A
publication date: 1996-12-01T00:00:00Z
review text: Let \(r,s\) be positive integers satisfying \(r>s\), \(2|r\) and \(\text{gcd} (r,s) =1\). The author proves that if \(2|r\), \(r\geq 81s\) and \(s\equiv 3\pmod 4\), then the equation \[ (r^2-s^2)^x +(2rs)^y =(r^2+s^2)^z \] has as the only solution \((x,y,z) =(2,2,2)\).
Mathematics Subject Classification ID: 11D61
Mathematics Subject Classification ID: 11J86
zbMATH DE Number: 952365
zbMATH Keywords: Jeśmanowicz' conjecture
zbMATH Keywords: Pythagorean numbers
zbMATH Keywords: exponential equations
author: Le Maohua
reviewed by: Edward L. Cohen
MaRDI profile type: Publication
full work available at URL: pjaa.72.97
OpenAlex ID: W1966600330
cites work: Q4864620
cites work: Q3239359
cites work: Linear forms in two logarithms and interpolation determinants
cites work: A note on Jeśmanowicz' conjecture
cites work: Q3904661
cites work: On a conjecture on Pythagorean numbers. II
Wikidata QID: Q114023240
DOI: 10.3792/PJAA.72.97
description: scientific article; zbMATH DE number 952365