On the Diophantine equation \(x^2+2=y^n\)
type: Item
instance of: scholarly article
title: On the Diophantine equation \(x^2+2=y^n\)
zbMATH Open document ID: 0968.11021
published in: Archiv der Mathematik
publication date: 2001-08-13T00:00:00Z
review text: The author gives an elementary proof of the fact that the only solutions of the Diophantine equation \(x^2+2=y^n\) for \(n>1\) are \((x,y,n)=(\pm 5,3,3)\). The first proof of this result is due to Nagell, but he uses a non elementary result of Mahler on binary quadratic forms. An important tool of the present proof is the curious polynomial identity: \[ \sum_{j=0}^{[k/2]}(-1)^j {k-j \choose j} (XY)^j(X+Y)^{k-2j}=\sum_{d=0}^k X^dY^{k-d}. \]
reviewed by: Maurice Mignotte
Mathematics Subject Classification ID: 11D61
zbMATH DE Number: 1484681
zbMATH Keywords: Nagell equation
zbMATH Keywords: exponential Diophantine equations
author: Balasubramanian Sury
MaRDI profile type: Publication
full work available at URL: s000130050454
OpenAlex ID: W2035104751
DOI: 10.1007/S000130050454
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description: scientific article; zbMATH DE number 1484681