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

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 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 -