Geodesic
Criteria for Simultaneous Solutions of X 2 − DY 2 = c and x 2 − Dy 2 = −c
Canadian mathematical bulletin, Tome 45 (2002) no. 3, pp. 428-435

Voir la notice de l'article provenant de la source Cambridge

DOI

The purpose of this article is to provide criteria for the simultaneous solvability of the Diophantine equations ${{X}^{2}}-D{{Y}^{2}}\,=\,c$ and ${{x}^{2}}-D{{y}^{2}}=-c$ when $c\,\in \,\mathbb{Z}$ , and $D\,\in \,\mathbb{N}$ is not a perfect square. This continues work in [6]–[8].
DOI : 10.4153/CMB-2002-045-2
Mots-clés : 11A55, 11R11, 11D09, continued fractions, Diophantine equations, fundamental units, simultaneous solutions 
Mollin, R. A. Criteria for Simultaneous Solutions of X 2 − DY 2 = c and x 2 − Dy 2 = −c. Canadian mathematical bulletin, Tome 45 (2002) no. 3, pp. 428-435. doi: 10.4153/CMB-2002-045-2
@article{10_4153_CMB_2002_045_2,
     author = {Mollin, R. A.},
     title = {Criteria for {Simultaneous} {Solutions} of {X} 2 \ensuremath{-} {DY} 2 = c and x 2 \ensuremath{-} {Dy} 2 = \ensuremath{-}c},
     journal = {Canadian mathematical bulletin},
     pages = {428--435},
     year = {2002},
     volume = {45},
     number = {3},
     doi = {10.4153/CMB-2002-045-2},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-2002-045-2/}
}
TY  - JOUR
AU  - Mollin, R. A.
TI  - Criteria for Simultaneous Solutions of X 2 − DY 2 = c and x 2 − Dy 2 = −c
JO  - Canadian mathematical bulletin
PY  - 2002
SP  - 428
EP  - 435
VL  - 45
IS  - 3
UR  - http://geodesic.mathdoc.fr/articles/10.4153/CMB-2002-045-2/
DO  - 10.4153/CMB-2002-045-2
ID  - 10_4153_CMB_2002_045_2
ER  - 
%0 Journal Article
%A Mollin, R. A.
%T Criteria for Simultaneous Solutions of X 2 − DY 2 = c and x 2 − Dy 2 = −c
%J Canadian mathematical bulletin
%D 2002
%P 428-435
%V 45
%N 3
%U http://geodesic.mathdoc.fr/articles/10.4153/CMB-2002-045-2/
%R 10.4153/CMB-2002-045-2
%F 10_4153_CMB_2002_045_2

Cité par Sources :