Finiteness results for Diophantine triples with repdigit values

2015/02/19 by Attila Bérczes, Bérczes, Attila, Florian Luca +5
Mathematics · #11D61 #FOS: Mathematics #Number Theory (math.NT) #math.NT #msc:11D61

paper · pdf · doi:10.48550/arxiv.1502.05550

arxiv created 2015/08/28 · arxiv updated 2015/08/31

Abstract

Let g≥ 2 be an integer and \mathcal R_g⊂ \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)∈ \mathbb N³ 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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