A note on the diophantine equation \(x^ 2+4D=y^ p\)
type: Item
instance of: scholarly article
title: A note on the diophantine equation \(x^ 2+4D=y^ p\)
zbMATH Open document ID: 0790.11023
DOI: 10.1007/BF01301534
published in: Monatshefte für Mathematik
publication date: 1994-06-26T00:00:00Z
full work available at URL: https://eudml.org/doc/178629
review text: For a positive square free integer \(D\), let \(h(-D)\) denote the class number of \(\mathbb{Q}(\sqrt{-D})\). Further, let \(p\) be an odd prime with \(h(- D)\not\equiv 0\pmod p\). The author shows that the diophantine equation \(x^ 2+ 4D= y^ p\) has no solution \((x,y)\in\mathbb{Z}^ 2\), provided \(p\in\{5,7\}\) or \(p> 3\cdot 10^ 6\). This result is a direct consequence of Theorem 5.11 of [\textit{M. Mignotte} and \textit{M. Waldschmidt}, Ann. Fac. Sci. Toulouse, V. Sér., Math. 1989, Spec., Issue 43-75 (1989; Zbl 0702.11044)].
Mathematics Subject Classification ID: 11D61
zbMATH DE Number: 508788
zbMATH Keywords: class number
zbMATH Keywords: exponential diophantine equation
author: Le Maohua
reviewed by: Roelof J. Stroeker
MaRDI profile type: Publication
cites work: Die diophantische Gleichung \(X^ 2 +4D = y^ p\) im Zusammenhang mit Klassenzahlen
cites work: On Square Fibonacci Numbers
cites work: Linear forms in two logarithms and Schneider's method (III)
OpenAlex ID: W2912481940
description: scientific article; zbMATH DE number 508788