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An Elementary Algorithm for Solving a Diophantine Equation of Degree Fourth with Runge’s Condition

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Publication:5853396
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DOI10.17516/1997-1397-2019-12-3-331-341zbMath1465.11235OpenAlexW2948594721MaRDI QIDQ5853396

Maria I. Medvedeva, Nikolay N. Osipov

Publication date: 18 March 2021

Published in: Journal of Siberian Federal University. Mathematics & Physics (Search for Journal in Brave)

Full work available at URL: http://mathnet.ru/eng/jsfu765


zbMATH Keywords

Diophantine equationRunge's method


Mathematics Subject Classification ID

Number-theoretic algorithms; complexity (11Y16) Cubic and quartic Diophantine equations (11D25)


Related Items

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



Cites Work

  • Unnamed Item
  • A simple method for solving the Diophantine equation \(Y^2=X^4+aX^3+bX^2+cX+d\)
  • Classical diophantine equations
  • ESTIMATES FOR THE SOLUTIONS OF CERTAIN DIOPHANTINE EQUATIONS BY RUNGE'S METHOD
  • Sur le théorème de Runge
  • A quantitative version of Runge's theorem on diophantine equations
  • On the Diophantine equation F(x)=G(y)
  • An Algorithmic Implementation of Runge’s Method for Cubic Diophantine Equations
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