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arXiv · 1502.05550

Finiteness results for Diophantine triples with repdigit values

Attila Bérczes·Florian Luca·István Pink·Volker Ziegler
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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 $c<b<a$ such that $ab+1,ac+1$ and $ab+1$ lie in the set $\mathcal R_g$. In this paper, we prove effective finitness results for the set $\mathcal D_g$.

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Attila Bérczes, Florian Luca, István Pink, Volker Ziegler. 2015-02-19. Finiteness results for Diophantine triples with repdigit values. https://arxiv.org/abs/1502.05550

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