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 $g\ge 2$ 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 $\mathcal D_g$.
