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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
Authors: Mollin, R.
Keywords: Continued Fractions
Diophantine Equations
Fundamental Units
Simultaneous Solutions
Norm Form Equations
Issue Date: 2002
Publisher: Institute of Mathematics and Informatics Bulgarian Academy of Sciences
Citation: Serdica Mathematical Journal, Vol. 28, No 2, (2002), 175p-188p
Abstract: 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].
ISSN: 1310-6600
Appears in Collections:Volume 28 Number 2

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