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 University Press

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
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