On equations \((-1)^\alpha p^x+ (-1)^\beta (2^k(2p + 1))^y= z^2\) with Sophie Germain prime \(p\)
type: Item
instance of: scholarly article
title: On equations \((-1)^\alpha p^x+ (-1)^\beta (2^k(2p + 1))^y= z^2\) with Sophie Germain prime \(p\)
zbMATH Open document ID: 1548.11066
author: Yuan Li
author: Jing Zhang
author: Baoxing Liu
published in: Involve
publication date: 2024-09-02T00:00:00Z
Mathematics Subject Classification ID: 11D61
Mathematics Subject Classification ID: 11A15
Mathematics Subject Classification ID: 14H52
zbMATH DE Number: 7904869
zbMATH Keywords: Catalan equation
zbMATH Keywords: exponential Diophantine equation
zbMATH Keywords: Legendre symbol
zbMATH Keywords: Nagell-Ljunggren equation
zbMATH Keywords: quadratic reciprocity law
zbMATH Keywords: Sophie Germain prime
MaRDI profile type: Publication
cites work: Q3392441
cites work: Q5088745
cites work: On the Nagell-Ljunggren equation $(x^n - 1)/(x - 1) = y^q$
cites work: On the Diophantine equation \({x^ n-1\over x-1}=y^ q\).
cites work: Generating safe primes
cites work: A note on the diophantine equation $x² + b^y = c^z$
cites work: Q5784076
cites work: Primary cyclotomic units and a proof of Catalans conjecture
cites work: Q5301801
cites work: The Diophantine equation $x^2 + q^m =p^n$
cites work: On the diophantine equation $(x^m-1)/(x-1) = y^n$
cites work: Q4333104
cites work: On the diophantine equation $x^2 + b^y = c^z$
DOI: 10.2140/INVOLVE.2024.17.503
description: scientific article; zbMATH DE number 7904869