Finiteness results for Diophantine triples with repdigit values

• Autorzy: Attila Bérczes , Florian Luca , István Pink , Volker Ziegler
• Języki publikacji: EN

Abstrakty

EN

Let g ≥ 2 be an integer and $𝓡_g ⊂ ℕ$ be the set of repdigits in base g. Let $𝓓_g$ be the set of Diophantine triples with values in $𝓡_g$; that is, $𝓓_g$ 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 $𝓡_g$. We prove effective finiteness results for the set $𝓓_g$.

Kategorie tematyczne

• 11D61: Exponential equations

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Acta Arithmetica
• Rocznik: 2016
• Tom: 172
• Numer: 2
• Strony: 133-148

Daty

wydano

2016

Twórcy

autor

Attila Bérczes

• Institute of Mathematics, University of Debrecen, P.O. Box 12, H-4010 Debrecen, Hungary

autor

Florian Luca

• School of Mathematics, University of the Witwatersrand, Private Bag X3, Wits 2050, Johannesburg, South Africa

autor

István Pink

• Institute of Mathematics, University of Debrecen, P.O. Box 12, H-4010 Debrecen, Hungary
• University of Salzburg, Hellbrunnerstrasse 34/I, A-5020 Salzburg, Austria

autor

Volker Ziegler

• University of Salzburg, Hellbrunnerstrasse 34/I, A-5020 Salzburg, Austria

Identyfikatory

DOI

10.4064/aa8089-12-2015