Continued Fractions Diophantine Equations Fundamental Units Simultaneous Solutions Ideals Norm Form Equations
Institute of Mathematics and Informatics Bulgarian Academy of Sciences
Serdica Mathematical Journal, Vol. 28, No 2, (2002), 175p-188p
This article provides necessary and sufficient conditions for
both of the Diophantine equations X^2 − DY^2 = m1 and x^2 − Dy^2 = m2
to have primitive solutions when m1 , m2 ∈ Z, and D ∈ N is not a perfect
square. This is given in terms of the ideal theory of the underlying real
quadratic order Z[√D].