 

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
Aa^{x}  Bb^{y}=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 FranceMexico ANUIESECOS M01M02.


Author information
Yann Bugeaud:
Université Louis Pasteur, UFR de mathématiques, 7 rue René Descartes, 67084 Strasbourg, France
bugeaud@math.ustrasbg.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

