# 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 (2002)

- Volume: 28, Issue: 2, page 175-188
- ISSN: 1310-6600

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topMollin, 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 28.2 (2002): 175-188. <http://eudml.org/doc/11554>.

@article{Mollin2002,

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].},

author = {Mollin, R.},

journal = {Serdica Mathematical Journal},

keywords = {Continued Fractions; Diophantine Equations; Fundamental Units; Simultaneous Solutions; Ideals; Norm Form Equations; primitive solution; binary quadratic Diophantine equation; fundamental unit},

language = {eng},

number = {2},

pages = {175-188},

publisher = {Institute of Mathematics and Informatics Bulgarian Academy of Sciences},

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},

url = {http://eudml.org/doc/11554},

volume = {28},

year = {2002},

}

TY - JOUR

AU - Mollin, R.

TI - 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

JO - Serdica Mathematical Journal

PY - 2002

PB - Institute of Mathematics and Informatics Bulgarian Academy of Sciences

VL - 28

IS - 2

SP - 175

EP - 188

AB - 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].

LA - eng

KW - Continued Fractions; Diophantine Equations; Fundamental Units; Simultaneous Solutions; Ideals; Norm Form Equations; primitive solution; binary quadratic Diophantine equation; fundamental unit

UR - http://eudml.org/doc/11554

ER -

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