An algorithm for solving a family of fourth-degree Diophantine equations that satisfy Runge's condition

DOI10.1134/S0361768821010060zbMath1476.11149OpenAlexW3130333409MaRDI QIDQ2027843

Nikolay N. Osipov, Alexey A. Kytmanov

Publication date: 28 May 2021

Published in: Programming and Computer Software (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1134/s0361768821010060

zbMATH Keywords

Diophantine equationRunge's method

Mathematics Subject Classification ID

Computer solution of Diophantine equations (11Y50) Cubic and quartic Diophantine equations (11D25)

Uses Software

• desing
• PGeomlib
• geom

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• A simple method for solving the Diophantine equation \(Y^2=X^4+aX^3+bX^2+cX+d\)
• Resolution of an algebraic singularity by power geometry algorithms
• Mechanical proof of planimetric theorems of rational type
• An algorithm for solving a quartic Diophantine equation satisfying Runge's condition
• Auxiliary Polynomials in Number Theory
• A quantitative version of Runge's theorem on diophantine equations
• Solving elliptic diophantine equations: the general cubic case
• On the Diophantine equation F(x)=G(y)
• 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

This page was built for publication: An algorithm for solving a family of fourth-degree Diophantine equations that satisfy Runge's condition