On the resolution of index form equations in biquadratic number fields. II

DOI10.1016/0022-314X(91)90091-OzbMath0726.11023OpenAlexW4206738522MaRDI QIDQ802648

Attila Pethoe, István Gaál, Michael E. Pohst

Publication date: 1991

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

Full work available at URL: https://doi.org/10.1016/0022-314x(91)90091-o

zbMATH Keywords

upper boundBaker's methodindex form equationscyclic biquadratic number fieldlinear form in logarithms of algebraic numbersLLL-lattice basis reduction algorithm

Mathematics Subject Classification ID

Computer solution of Diophantine equations (11Y50) Cubic and quartic extensions (11R16) Linear forms in logarithms; Baker's method (11J86) Diophantine equations (11D99)

Related Items (8)

Monogenic biquadratic fields ⋮ On the Resolution of Index Form Equations in Dihedral Quartic Number Fields ⋮ Two families of monogenic $S_4$ quartic number fields ⋮ The Solution of Triangularly Connected Decomposable Form Equations ⋮ Optimal systems of fundamental \(S\)-units for LLL-reduction ⋮ Computing all monogeneous mixed dihedral quartic extensions of a quadratic field ⋮ Establishing the minimal index in a parametric family of bicyclic biquadratic fields ⋮ Norm form equations and linear divisibility sequences

Cites Work

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• On the resolution of index form equations in biquadratic number fields. I
• On the indices and integral bases of non-cyclic but Abelian biquadratic fields
• On cyclic biquadratic fields related to a problem of Hasse
• Factoring polynomials with rational coefficients
• Berechnung unabhängiger Einheiten und Klassenzahlen in total reellen biquadratischen Zahlkörpern
• The diophantine equation \(y^2+k=x^3\).
• On Mordell's Equation y 2 - k = x 3 : A Problem of Stolarsky
• A lower bound for linear forms in logarithms
• THE EQUATIONS 3x²−2 = y² AND 8x²−7 = z²

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