A note on the number of solutions of the generalized Ramanujan-Nagell equation \(D_ 1x^ 2+D_ 2=4p^ n\)
type: Item
instance of: scholarly article
title: A note on the number of solutions of the generalized Ramanujan-Nagell equation \(D_ 1x^ 2+D_ 2=4p^ n\)
zbMATH Open document ID: 0869.11029
author: Le Maohua
published in: Journal of Number Theory
publication date: 1997-09-01T00:00:00Z
review text: Let \(D_1\), \(D_2\) be positive integers with \(2\nmid D_1D_2\) and \(\text{gcd} (D_1, D_2)=1\). Let \(p\) be a prime with \(p\nmid D_1D_2\). It is proved that the generalized Ramanujan-Nagell equation of the title has at most two positive integer solutions \((x,n)\) except for the cases \((D_1,D_2,p) =(1,7,2)\), \((3,5,2)\), \((1,11,3)\) and \((1,19,5)\).
Mathematics Subject Classification ID: 11D61
zbMATH DE Number: 992095
zbMATH Keywords: number of solutions
zbMATH Keywords: exponential diophantine equations
zbMATH Keywords: generalized Ramanujan-Nagell equation
reviewed by: Edward L. Cohen
MaRDI profile type: Publication
full work available at URL: jnth.1997.2019
OpenAlex ID: W2076404734
DOI: 10.1006/JNTH.1997.2019
description: scientific article; zbMATH DE number 992095