K. Kashihara, EXPLICIT COMPLETE SOLUTION IN INTEGERS OF A CLASS OF EQUATIONS (AX(2)-B)(AY(2)-B)=Z(2)-C, Manuscripta mathematica, 80(4), 1993, pp. 373-392
In this paper we will study the equation for arbitrary integers a not-
equal 0, c and b = +/- 1, +/- 2 or +/- 4. When b = +/- 4, we suppose c
is divisible by 4. The paper will provide one with a method for findi
ng algorithmically all integral non-trivial solutions of the title equ
ations, where an explicit unit of Q(square-root a2n2 - ab) plays an im
portant role.