On the Fermat-type equation \(x^3+y^3=z^p\)

DOI10.4171/CMH/386zbMath1419.11058arXiv1601.06361MaRDI QIDQ290755

Nuno Freitas

Publication date: 3 June 2016

Published in: Commentarii Mathematici Helvetici (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1601.06361

zbMATH Keywords

elliptic curvesgeneralized Fermat equationsymplectic isomorphism

Mathematics Subject Classification ID

Higher degree equations; Fermat's equation (11D41) Elliptic curves over local fields (11G07)

Related Items (8)

Summation formula inequalities for eigenvalues of the perturbed harmonic oscillator ⋮ An application of the symplectic argument to some Fermat-type equations ⋮ On the symplectic type of isomorphisms of the 𝑝-torsion of elliptic curves ⋮ Some extensions of the modular method and Fermat equations of signature \((13,13,n)\) ⋮ AN APPLICATION OF THE MODULAR METHOD AND THE SYMPLECTIC ARGUMENT TO A LEBESGUE–NAGELL EQUATION ⋮ Sums of two cubes as twisted perfect powers, revisited ⋮ The generalized Fermat equation with exponents 2, 3, ⋮ Rational periodic points of xd + c and Fermat–Catalan equations

Cites Work

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• Perfect powers expressible as sums of two cubes
• Twists of \(X(7)\) and primitive solutions to \(x^2+y^3=z^7\)
• Modular elliptic curves and Fermat's Last Theorem
• Recipes to Fermat-type equations of the form \(x^r + y^r =Cz^p\)
• Good reduction of abelian varieties
• The Arithmetic of Elliptic Curves
• Courbes de Fermat: résultats et problèmes
• Local invariants of isogenous elliptic curves
• On a question of B. Mazur

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