Integral solutions of the equation in the quadratic realms of rationality
Harris Hancock (1921)
Journal de Mathématiques Pures et Appliquées
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Harris Hancock (1921)
Journal de Mathématiques Pures et Appliquées
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Andrej Dujella (1998)
Acta Mathematica et Informatica Universitatis Ostraviensis
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Daniel Shanks, Peter Weinberger (1972)
Acta Arithmetica
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Francesco Veneziano (2011)
Rendiconti del Seminario Matematico della Università di Padova
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Mollin, R. (2002)
Serdica Mathematical Journal
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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].
R. Mollin, C. Small, K. Varadarajan, P. Walsh (1987)
Acta Arithmetica
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