New York Journal of Mathematics
Volume 12 (2006) 193-217


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

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.


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

Florian Luca:
Instituto de Matem{á}ticas, Universidad Nacional Autónoma de M{é}xico, C.P. 58089, Morelia, Michoac{á}n, M{é}xico