The equations \(2^N\pm 2^M\pm 2^L=z^2\)
type: Item
instance of: scholarly article
title: The equations \(2^N\pm 2^M\pm 2^L=z^2\)
zbMATH Open document ID: 1014.11022
DOI: 10.1016/S0019-3577(02)90011-X
author: László Szalay
published in: Indagationes Mathematicae. New Series
publication date: 2003-06-05T00:00:00Z
review text: The author completely solves the equations \(2^N\pm 2^M\pm 2^L=z^2\), which can easily be reduced to the two cases \(2^n\pm 2^m\pm 1=z^2\) and \(2^n\pm 2^m\pm 2 =z^2\). This problem was posed by R. Tijdeman. In the second case, the solution is rather simple, as well as for the subcase \(2^n\pm 2^m-1=z^2\). But the solution of the particular case \(2^n+2^m+1=z^2\) is based on some deep results of F. Beukers (1981) and needs a detailed study.
Mathematics Subject Classification ID: 11D61
zbMATH DE Number: 1893635
zbMATH Keywords: binary expansion
zbMATH Keywords: squares
zbMATH Keywords: exponential Diophantine equations
reviewed by: Maurice Mignotte
MaRDI profile type: Publication
cites work: Q3269226
cites work: On the generalized Ramanujan-Nagell equation I
cites work: Q5611904
cites work: Über eine Diophantische Gleichung von Ramanujan-Nagell und ihre Verallgemeinerung
cites work: The diophantine equation \(x^2+7=2^n\)
cites work: Q3744223
full work available at URL: s0019-3577(02)90011-x
OpenAlex ID: W2015805705
description: scientific article; zbMATH DE number 1893635