Some exponential diophantine equations. I: The equation \(D_1x^2 - D_2y^2 = \lambda k^z\)
type: Item
instance of: scholarly article
title: Some exponential diophantine equations. I: The equation \(D_1x^2 - D_2y^2 = \lambda k^z\)
zbMATH Open document ID: 0852.11015
published in: Journal of Number Theory
publication date: 1996-08-05T00:00:00Z
review text: Let \(D\) be a non-square integer, and let \(D_1\), \(D_2\) be integers satisfying \(D_1 D_2= D\) with \(D_1>0\) and \(\gcd(D_1, D_2) =1\). Let \(k\) be an integer with \(|k|> 1\) and \(\gcd(D, k)=1\). The author gives some explicit formulas for all integer solutions \((x, y, z)\) of the equation in the title when \(\gcd(x, y) =1\), \(z>0\) and \(\lambda=1\text{ or }4\).
Mathematics Subject Classification ID: 11D61
zbMATH DE Number: 844632
zbMATH Keywords: exponential diophantine equations
zbMATH Keywords: explicit formulas for integer solutions
author: Le Maohua
reviewed by: Edward L. Cohen
MaRDI profile type: Publication
full work available at URL: jnth.1995.1138
OpenAlex ID: W1566904357
DOI: 10.1006/JNTH.1995.1138
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description: scientific article; zbMATH DE number 844632