1Institute of Mathematics University of Debrecen P.O. Box 12 H-4010 Debrecen, Hungary 2School of Mathematics University of the Witwatersrand Private Bag X3, Wits 2050 Johannesburg, South Africa 3Institute of Mathematics University of Debrecen P.O. Box 12 H-4010 Debrecen, Hungary and University of Salzburg Hellbrunnerstrasse 34/I A-5020 Salzburg, Austria 4University of Salzburg Hellbrunnerstrasse 34/I A-5020 Salzburg, Austria
Acta Arithmetica, Tome 172 (2016) no. 2, pp. 133-148
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 $\mathcal D_g$.
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
Affiliations des auteurs :
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},
year = {2016},
volume = {172},
number = {2},
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
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
%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
