SOLVING ELLIPTIC DIOPHANTINE EQUATIONS AVOIDING THUE EQUATIONS AND ELLIPTIC LOGARITHMS

Authors
DEWEGER BMM
Citation
Bmm. Deweger, SOLVING ELLIPTIC DIOPHANTINE EQUATIONS AVOIDING THUE EQUATIONS AND ELLIPTIC LOGARITHMS, Experimental mathematics, 7(3), 1998, pp. 243-256
Citations number
16
Categorie Soggetti
Mathematics,Mathematics
Journal title
Experimental mathematics → ACNP
ISSN journal
10586458
Volume
7
Issue
3
Year of publication
1998
Pages
243 - 256
Database
ISI
SICI code
1058-6458(1998)7:3<243:SEDEAT>2.0.ZU;2-V
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 suggeste d to us by Yu. Bilu, and is shown to be in some cases more efficient t han other general purpose methods for solving such equations, namely t he elliptic logarithms method and the use of Thue equations.