The Fermat equation over quadratic fields

DOI10.1016/0022-314X(84)90096-9zbMath0538.10015OpenAlexW2151136399MaRDI QIDQ793077

Fred H. Hao, Charles J. Parry

Publication date: 1984

Published in: Journal of Number Theory (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0022-314x(84)90096-9

zbMATH Keywords

quadratic number fieldFermat equationcase I of Fermat's last theoremcase IIm-regular prime

Mathematics Subject Classification ID

Quadratic extensions (11R11) Higher degree equations; Fermat's equation (11D41)

Related Items (11)

Équation de Fermat et nombres premiers inertes ⋮ Ramanujan type congruences for modular forms of several variables ⋮ Fermat’s Last Theorem and modular curves over real quadratic fields ⋮ The asymptotic Fermat’s Last Theorem for five-sixths of real quadratic fields ⋮ Fermat’s Last Theorem over and ⋮ The \(abc\)-conjecture for algebraic numbers ⋮ The relative class numbers of certain imaginary abelian number fields and determinants ⋮ The Fermat theorem over \(\mathbb Q(\sqrt{5})\) ⋮ The Fermat equation over \(\mathbb Q(\sqrt 2)\) ⋮ Norm residue symbol and the first case of Fermat's equation ⋮ On Fermat's equation over some quadratic imaginary number fields

Cites Work

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• Die Unmöglichkeit von \(x^ 6 + y^ 6 = z^ 6\) und \(x^ 9 + y^ 9 = z^ 9\) in quadratischen Körpern
• Units of algebraic numberfields
• Über die Möglichkeit einiger diophantischer Gleichungen 3. und 4. Grades in quadratischen Körpern
• Weitere Ergebnisse über \(x^ 3+y^ 3=z^ 3\) in quadratischen Körpern
• Ein zweiter Fall der Unmöglichkeit von \(x^3+y^3=z^3\) in quadratischen Körpern mit durch 3 teilbarer Klassenzahl
• Unmöglichkeitskernzahlen der kubischen Fermatgleichung mit Primfaktoren der Art 3n + 1.
• On the Class Number of Relative Quadratic Fields

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