## Experimental Mathematics

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

### Solving elliptic Diophantine equations avoiding Thue equations and elliptic logarithms

#### 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