Letter to the editor: ''Diophantine equation \(x^ 3-y^ 2=k\) and Hall's conjecture''
type: Item
instance of: scholarly article
title: Letter to the editor: ''Diophantine equation \(x^ 3-y^ 2=k\) and Hall's conjecture''
zbMATH Open document ID: 0567.10011
DOI: 10.1007/BF01141949
author: L. V. Danilov
published in: Mathematical Notes
publication date: 1984-01-01T00:00:00Z
review text: In the article mentioned in the title [Mat. Zametki 32, 273-275 (1982; Zbl 0499.10016)], there is an inaccuracy, whose removal improves by a factor of 2 the constant in the right-hand side of (5). It follows from the text of the article that on p. 274 we should have in the right-hand side of Eq. (9) -216 \(P_ m+432\), and hence we have a stronger form of the theorem. After the publication of this article, the author noticed that the constant in the theorem could again be significantly decreased, in order to give the following theorem. The inequalities \[ 0<| x^ 3-y^ 2| <0.97 | x|^{0,5} \] have infinitely many solutions in integers x and y.
Mathematics Subject Classification ID: 11D25
zbMATH DE Number: 3904667
zbMATH Keywords: cubic diophantine equation
zbMATH Keywords: Hall's second conjecture
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1007/bf01141949
OpenAlex ID: W4233861272
description: scientific article; zbMATH DE number 3904667