Finiteness results for Diophantine triples with repdigit values

Attila Bérczes; Florian Luca; István Pink; Volker Ziegler

Attila Bérczes ; Florian Luca ; István Pink ; Volker Ziegler

Acta Arithmetica, Tome 172 (2016), p. 133-148 / Harvested from The Polish Digital Mathematics Library

Résumé

Let g ≥ 2 be an integer and $_{g} \subset ℕ$ be the set of repdigits in base g. Let $_{g}$ be the set of Diophantine triples with values in $_{g}$ ; that is, $_{g}$ is the set of all triples (a,b,c) ∈ ℕ³ with c < b < a such that ab + 1, ac + 1 and bc + 1 lie in the set $_{g}$ . We prove effective finiteness results for the set $_{g}$ .

Publié le : 2016-01-01

Zbl 06545344

EUDML-ID : urn:eudml:doc:279043

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     author = {Attila B\'erczes and Florian Luca and Istv\'an Pink and Volker Ziegler},
     title = {Finiteness results for Diophantine triples with repdigit values},
     journal = {Acta Arithmetica},
     volume = {172},
     year = {2016},
     pages = {133-148},
     zbl = {06545344},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-aa8089-12-2015}
}

Attila Bérczes; Florian Luca; István Pink; Volker Ziegler. Finiteness results for Diophantine triples with repdigit values. Acta Arithmetica, Tome 172 (2016) pp. 133-148. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-aa8089-12-2015/