Experimental Mathematics

Solving elliptic Diophantine equations avoiding Thue equations and elliptic logarithms

Benjamin M. M. de Weger

Abstract

We determine the solutions in integers of the equation $ y^2 = ( x + p ) ( x^2 + p^2 ) $ for $ p = 167$, $223$, $337$, $1201$. The method used was suggested to us by Yu. Bilu, and is shown to be in some cases more efficient than other general purpose methods for solving such equations, namely the elliptic logarithms method and the use of Thue equations.

Article information

Source
Experiment. Math., Volume 7, Issue 3 (1998), 243-256.

Dates
First available in Project Euclid: 14 March 2003

Permanent link to this document
https://projecteuclid.org/euclid.em/1047674206

Mathematical Reviews number (MathSciNet)
MR1676758

Zentralblatt MATH identifier
0921.11076

Subjects
Primary: 11Y50: Computer solution of Diophantine equations
Secondary: 11D25: Cubic and quartic equations

Citation

de Weger, Benjamin M. M. Solving elliptic Diophantine equations avoiding Thue equations and elliptic logarithms. Experiment. Math. 7 (1998), no. 3, 243--256. https://projecteuclid.org/euclid.em/1047674206


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