Geodesic
On the extension of the Diophantine pair $\{1,3\}$ in $\Bbb Z[\sqrt d]$
Journal of integer sequences, Tome 13 (2010) no. 9.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: In this paper, we consider Diophantine triples of the form ${1,3,c}$ in the ring $Z[\sqrt d]$. We prove that the Diophantine pair ${1,3}$ cannot be extended to the Diophantine quintuple in $Z[\sqrt d]$ with $d 0$ and $d \ne -2$.
Classification : 11D09, 11R11
Keywords: Diophantine sets, quadratic fields, pellian equations 
@article{JIS_2010__13_9_a3,
     author = {Franu\v{s}i\'c, Zrinka},
     title = {On the extension of the {Diophantine} pair $\{1,3\}$ in $\Bbb Z[\sqrt d]$},
     journal = {Journal of integer sequences},
     publisher = {mathdoc},
     volume = {13},
     number = {9},
     year = {2010},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/JIS_2010__13_9_a3/}
}
TY  - JOUR
AU  - Franušić, Zrinka
TI  - On the extension of the Diophantine pair $\{1,3\}$ in $\Bbb Z[\sqrt d]$
JO  - Journal of integer sequences
PY  - 2010
VL  - 13
IS  - 9
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/JIS_2010__13_9_a3/
LA  - en
ID  - JIS_2010__13_9_a3
ER  - 
%0 Journal Article
%A Franušić, Zrinka
%T On the extension of the Diophantine pair $\{1,3\}$ in $\Bbb Z[\sqrt d]$
%J Journal of integer sequences
%D 2010
%V 13
%N 9
%I mathdoc
%U http://geodesic.mathdoc.fr/item/JIS_2010__13_9_a3/
%G en
%F JIS_2010__13_9_a3
Franušić, Zrinka. On the extension of the Diophantine pair $\{1,3\}$ in $\Bbb Z[\sqrt d]$. Journal of integer sequences, Tome 13 (2010) no. 9. http://geodesic.mathdoc.fr/item/JIS_2010__13_9_a3/