Geodesic
Finiteness results for Diophantine triples with repdigit values
Attila Bérczes1 ; Florian Luca2 ; István Pink3 ; Volker Ziegler4
1 Institute of Mathematics University of Debrecen P.O. Box 12 H-4010 Debrecen, Hungary
2 School of Mathematics University of the Witwatersrand Private Bag X3, Wits 2050 Johannesburg, South Africa
3 Institute of Mathematics University of Debrecen P.O. Box 12 H-4010 Debrecen, Hungary and University of Salzburg Hellbrunnerstrasse 34/I A-5020 Salzburg, Austria
4 University of Salzburg Hellbrunnerstrasse 34/I A-5020 Salzburg, Austria
Acta Arithmetica, Tome 172 (2016) no. 2, pp. 133-148.

Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences

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 $\mathcal D_g$.
DOI : 10.4064/aa8089-12-2015
Keywords: integer mathcal subset mathbb set repdigits base mathcal set diophantine triples values mathcal mathcal set triples mathbb lie set mathcal prove effective finiteness results set mathcal

Attila Bérczes 1 ; Florian Luca 2 ; István Pink 3 ; Volker Ziegler 4

1 Institute of Mathematics University of Debrecen P.O. Box 12 H-4010 Debrecen, Hungary
2 School of Mathematics University of the Witwatersrand Private Bag X3, Wits 2050 Johannesburg, South Africa
3 Institute of Mathematics University of Debrecen P.O. Box 12 H-4010 Debrecen, Hungary and University of Salzburg Hellbrunnerstrasse 34/I A-5020 Salzburg, Austria
4 University of Salzburg Hellbrunnerstrasse 34/I A-5020 Salzburg, Austria 
@article{10_4064_aa8089_12_2015,
     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},
     pages = {133--148},
     publisher = {mathdoc},
     volume = {172},
     number = {2},
     year = {2016},
     doi = {10.4064/aa8089-12-2015},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.4064/aa8089-12-2015/}
}
TY  - JOUR
AU  - Attila Bérczes
AU  - Florian Luca
AU  - István Pink
AU  - Volker Ziegler
TI  - Finiteness results for Diophantine triples with repdigit values
JO  - Acta Arithmetica
PY  - 2016
SP  - 133
EP  - 148
VL  - 172
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/articles/10.4064/aa8089-12-2015/
DO  - 10.4064/aa8089-12-2015
LA  - en
ID  - 10_4064_aa8089_12_2015
ER  - 
%0 Journal Article
%A Attila Bérczes
%A Florian Luca
%A István Pink
%A Volker Ziegler
%T Finiteness results for Diophantine triples with repdigit values
%J Acta Arithmetica
%D 2016
%P 133-148
%V 172
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/articles/10.4064/aa8089-12-2015/
%R 10.4064/aa8089-12-2015
%G en
%F 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) no. 2, pp. 133-148. doi : 10.4064/aa8089-12-2015. http://geodesic.mathdoc.fr/articles/10.4064/aa8089-12-2015/

Cité par Sources :