ACTA MATHEMATICA UNIVERSITATIS COMENIANAE
Vol. LXXI, 2(2002)
p. 121
The Diophantine Equation AX2-BY2=C Solved Via
Continued Fractions
R. A. Mollin, K. Cheng and B. Goddard
Abstract.
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].
AMS subject classification:
11A55 11R11 11D09
Keywords:
Continued fractions, Diophantine equations, fundamental units
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