Solutions of Diophantine equations and divisibility of class numbers of complex quadratic fields

DOI10.1017/S0017089500031438zbMath0859.11058MaRDI QIDQ4884422

Richard A. Mollin

Publication date: 9 April 1997

Published in: Glasgow Mathematical Journal (Search for Journal in Brave)

zbMATH Keywords

divisibility of class numberscomplex quadratic fields

Mathematics Subject Classification ID

Quadratic extensions (11R11) Quadratic and bilinear Diophantine equations (11D09) Class numbers, class groups, discriminants (11R29)

Related Items (6)

On the divisibility of class numbers of quadratic fields and the solvability of Diophantine equations ⋮ Existence of an infinite family of pairs of quadratic fields \(\mathbb{Q}(\sqrt{m_1D})\) and \(\mathbb{Q}(\sqrt{m_2D})\) whose class numbers are both divisible by 3 or both indivisible by 3 ⋮ Parametrization of the quadratic fields whose class numbers are divisible by three ⋮ A note on the divisibility of class numbers of imaginary quadratic fields \(\mathbb Q(\sqrt{a^2 - k^n})\) ⋮ THE DIVISIBILITY OF THE CLASS NUMBER OF THE IMAGINARY QUADRATIC FIELD ⋮ Notes on the divisibility of the class numbers of imaginary quadratic fields \(\mathbb {Q}(\sqrt{3^{2e} - 4k^n})\)

Cites Work

• The Diophantine equation \(x^2+11=3^n\) and a related sequence
• Some results on the Mordell-Weil group of the Jacobian of the Fermat curve
• Orders in quadratic fields. III
• On the divisibility of the class number of quadratic fields
• Diophantine equations and class numbers
• On the divisibility of the class number of imaginary quadratic fields

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