A simple method for solving the Diophantine equation \(Y^2=X^4+aX^3+bX^2+cX+d\)

DOI10.1007/s000170050053zbMath0952.11005OpenAlexW1486332446MaRDI QIDQ1296766

Dimitrios Poulakis

Publication date: 21 November 1999

Published in: Elemente der Mathematik (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s000170050053

zbMATH Keywords

hyperelliptic equation

Mathematics Subject Classification ID

Diophantine inequalities (11D75) Cubic and quartic Diophantine equations (11D25)

Related Items (8)

Polynomials with values which are powers of integers ⋮ On the Diophantine equation \(y^p = f(x_1, x_2,\ldots, x_r)\) ⋮ Unnamed Item ⋮ An algorithm for solving a family of fourth-degree Diophantine equations that satisfy Runge's condition ⋮ Integer points on the curve $Y^{2}=X^{3}\pm p^{k}X$ ⋮ An Algorithmic Implementation of Runge’s Method for Cubic Diophantine Equations ⋮ An Elementary Algorithm for Solving a Diophantine Equation of Degree Fourth with Runge’s Condition ⋮ Solving genus zero Diophantine equations with at most two infinite valuations

Cites Work

• Fermat's `primitive solutions' and some arithmetic of elliptic curves
• The Diophantine Equation f(x) = g(y)
• Solving elliptic diophantine equations by estimating linear forms in elliptic logarithms. The case of quartic equations

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