| |
|
Yann Bugeaud and Florian Luca
On Pillai's Diophantine equation
|
|
| Published: |
August 6, 2006 |
| Keywords: |
Diophantine equations, applications of linear forms in logarithms and the Subspace Theorem, ABC conjecture |
| Subject: |
11D61, 11D72, 11D45 |
|
|
Abstract
Let A, B, a, b and c be fixed nonzero integers.
We prove several results on the number of
solutions to Pillai's Diophantine equation
Aax - Bby=c in positive unknown integers x and y.
|
|
| Acknowledgements
This paper was written during a visit of the second author at the Université Louis Pasteur in Strasbourg in September 2004. He warmly thanks the Mathematical Department for its hospitality. Both authors were supported in part by the joint Project France-Mexico ANUIES-ECOS M01-M02.
|
|
| Author information
Yann Bugeaud:
Université Louis Pasteur, UFR de mathématiques, 7 rue René Descartes, 67084 Strasbourg, France
bugeaud@math.u-strasbg.fr
Florian Luca:
Instituto de Matem{á}ticas, Universidad Nacional Autónoma de M{é}xico, C.P. 58089, Morelia, Michoac{á}n, M{é}xico
fluca@matmor.unam.mx
|
|
