Geodesic
The Diophantine Equation AX 2 - BY 2 =C Solved Via Continued Fractions
Acta mathematica Universitatis Comenianae, Tome 71 (2002) no. 2 
R. A. Mollin; K. Cheng; B. Goddard. The Diophantine Equation AX 2 - BY 2 =C Solved Via 
Continued Fractions. Acta mathematica Universitatis Comenianae, Tome 71 (2002) no. 2. http://geodesic.mathdoc.fr/item/AMUC_2002_71_2_a0/
@article{AMUC_2002_71_2_a0,
     author = {R. A. Mollin and K. Cheng and B. Goddard},
     title = {The {Diophantine} {Equation} {AX} 2 - {BY} 2 {=C} {Solved} {Via} {
Continued} {Fractions}},
     journal = {Acta mathematica Universitatis Comenianae},
     year = {2002},
     volume = {71},
     number = {2},
     url = {http://geodesic.mathdoc.fr/item/AMUC_2002_71_2_a0/}
}
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AU  - K. Cheng
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Continued Fractions
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Continued Fractions
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Voir la notice de l'article provenant de la source Comenius University

The purpose of this article is to provide criteria for the solvability of the Diophantine equation $a^2X^2-bY^2=c$ in terms of the simple continued fraction expansion of $\sqrt{a^2b}$, and to explore criteria for the solvability of $AX^2-BY^2=C$ for given $A,B,C\in\N$ in the general case. This continues work in [9]–[11].