Geodesic
Ideal Criteria for both Ideal Criteria for both X2-dy2 = M1 And X2-dy2 = M2 to have Primitive Solutions for any Integers M1, M2 Prime to D > 0
Serdica Mathematical Journal, Tome 28 (2002) no. 2, pp. 175-188.

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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].
Keywords: Continued Fractions, Diophantine Equations, Fundamental Units, Simultaneous Solutions, Ideals, Norm Form Equations 
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     title = {Ideal {Criteria} for both {Ideal} {Criteria} for both {X2-dy2} = {M1} {And} {X2-dy2} = {M2} to have {Primitive} {Solutions} for any {Integers} {M1,} {M2} {Prime} to {D} > 0},
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Mollin, R. Ideal Criteria for both Ideal Criteria for both X2-dy2 = M1 And X2-dy2 = M2 to have Primitive Solutions for any Integers M1, M2 Prime to D > 0. Serdica Mathematical Journal, Tome 28 (2002) no. 2, pp. 175-188. http://geodesic.mathdoc.fr/item/SMJ2_2002_28_2_a5/