A simple method for solving the Diophantine equation \(Y^2=X^4+aX^3+bX^2+cX+d\)
type: Item
instance of: scholarly article
title: A simple method for solving the Diophantine equation \(Y^2=X^4+aX^3+bX^2+cX+d\)
zbMATH Open document ID: 0952.11005
author: Dimitros Poulakis
published in: Elemente der Mathematik
publication date: 1999-11-21T00:00:00Z
review text: The author gives intervals containing the solutions \(x\) of the title equation. The intervals are surprisingly short, depend only on the coefficients of the polynomial involved and make it possible to determine the solutions in many cases without computers. The proof is elementary.
reviewed by: István Gaál
Mathematics Subject Classification ID: 11D25
Mathematics Subject Classification ID: 11D75
zbMATH DE Number: 1319943
zbMATH Keywords: hyperelliptic equation
MaRDI profile type: Publication
full work available at URL: s000170050053
OpenAlex ID: W1486332446
cites work: The Diophantine Equation f(x) = g(y)
cites work: Fermat's `primitive solutions' and some arithmetic of elliptic curves
cites work: Solving elliptic diophantine equations by estimating linear forms in elliptic logarithms. The case of quartic equations
DOI: 10.1007/S000170050053
description: scientific article; zbMATH DE number 1319943