Elliptic binomial diophantine equations
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- by Roelof J. Stroeker and Benjamin M. M. de Weger PDF
- Math. Comp. 68 (1999), 1257-1281 Request permission
Abstract:
The complete sets of solutions of the equation $\binom {n}{k} = \binom {m}{\ell }$ are determined for the cases $(k,\ell ) = (2,3)$, $(2,4)$, $(2,6)$, $(2,8)$, $(3,4)$, $(3,6)$, $(4,6)$, $(4,8)$. In each of these cases the equation is reduced to an elliptic equation, which is solved by using linear forms in elliptic logarithms. In all but one case this is more or less routine, but in the remaining case ($(k,\ell ) = (3,6)$) we had to devise a new variant of the method.References
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Additional Information
- Roelof J. Stroeker
- Affiliation: Econometric Institute, Erasmus University Rotterdam, P.O. Box 1738, 3000 DR Rotterdam, The Netherlands
- Email: stroeker@few.eur.nl
- Benjamin M. M. de Weger
- Affiliation: Sportsingel 30, 2924 XN Krimpen aan den ijssel, The Neterlands
- Email: deweger@xs4all.nl
- Received by editor(s): October 16, 1997
- Published electronically: February 23, 1999
- Additional Notes: The second author’s research was supported by the Netherlands Mathematical Research Foundation SWON with financial aid from the Netherlands Organization for Scientific Research NWO
- © Copyright 1999 American Mathematical Society
- Journal: Math. Comp. 68 (1999), 1257-1281
- MSC (1991): Primary 11D25, 11G05; Secondary 11B65, 14H52
- DOI: https://doi.org/10.1090/S0025-5718-99-01047-9
- MathSciNet review: 1622097