Finiteness results for Diophantine triples with repdigit values
Volume 172 / 2016
Acta Arithmetica 172 (2016), 133-148
MSC: Primary 11D61.
DOI: 10.4064/aa8089-12-2015
Published online: 23 December 2015
Abstract
Let be an integer and \mathcal R_g\subset \mathbb{N} be the set of repdigits in base g. Let \mathcal D_g be the set of Diophantine triples with values in \mathcal R_g; that is, \mathcal D_g is the set of all triples (a,b,c)\in \mathbb{N}^3 with c \lt b \lt a such that ab+1, ac+1 and bc+1 lie in the set \mathcal R_g. We prove effective finiteness results for the set \mathcal D_g.
