Mathematics of Computation

Author(s): R. J. Stroeker; N. Tzanakis.
Journal: Math. Comp. 72 (2003), 1917-1933.
MSC (2000): Primary 11D41, 11G05
Posted: January 8, 2003
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Abstract: The elliptic logarithm method has been applied with great success to the problem of computing all integer solutions of equations of degree

and

defining elliptic curves. We extend this method to include any equation

, where $f\in\mathbb{Z}[u,v]$ is irreducible over $\overline{\mathbb{Q}}$ , defines a curve of genus

, but is otherwise of arbitrary shape and degree. We give a detailed description of the general features of our approach, and conclude with two rather unusual examples corresponding to equations of degree

and degree

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R. J. Stroeker
Affiliation: Econometric Institute, Erasmus University, P. O. Box 1738, 3000 DR Rotterdam, The Netherlands
Email: stroeker@few.eur.nl

N. Tzanakis
Affiliation: Department of Mathematics, University of Crete, Iraklion, Greece
Email: tzanakis@math.uch.gr

DOI: 10.1090/S0025-5718-03-01497-2
PII: S 0025-5718(03)01497-2
Keywords: Diophantine equation, elliptic curve, elliptic logarithm
Received by editor(s): January 28, 2002
Posted: January 8, 2003
Copyright of article: Copyright 2003, American Mathematical Society

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