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