Generalized Fermat equations: A miscellany (Q2941067)

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Language	Label	Description	Also known as
English	Generalized Fermat equations: A miscellany	scientific article

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scholarly article

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Generalized Fermat equations: A miscellany (English)

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Michael A. Bennett

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Sander R. Dahmen

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Soroosh Yazdani

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International Journal of Number Theory

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publication date

21 January 2015

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zbMATH Keywords

Fermat equations

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Galois representations

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\(\mathbb{Q}\)-curves

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multi-frey techniques

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MaRDI profile type

MaRDI publication profile

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The equation \(x^{2n}+y^{2n}=z^5\)

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Multi-Frey \(\mathbb Q\)-curves and the Diophantine equation \(a^2+b^6=c^n\)

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On the equation a<sup>3</sup>+ b<sup>3n</sup>= c<sup>2</sup>

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Klein forms and the generalized superelliptic equation

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THE DIOPHANTINE EQUATION A<sup>4</sup> + 2<sup>δ</sup>B<sup>2</sup> = C<sup>n</sup>

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Ternary Diophantine Equations via Galois Representations and Modular Forms

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Ternary Diophantine equations of signature (<i>p</i>, <i>p</i>, 3)

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The Diophantine equation \(Ax^ p+By^ q=Cz^ r\).

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Équations de Fermat de type (5, 5,<i>p</i>)

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Solving Fermat-type equations $x^5+y^5=dz^p$

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On the modularity of elliptic curves over 𝐐: Wild 3-adic exercises

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Primitive Integral Solutions to x2+y3=z10

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Chabauty methods using elliptic curves

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The primitive solutions to \(x^3+y^9=z^2\)

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A Multi-Frey Approach to Some Multi-Parameter Families of Diophantine Equations

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On the equation $s^2+y^{2p} = \alpha^3$

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On the equation a<sup>2</sup>+b<sup>2p</sup>= c<sup>5</sup>

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On the equations <i>a</i><sup>2</sup>−2<i>b</i><sup>6</sup>=<i>c</i><sup><i>p</i></sup> and <i>a</i><sup>2</sup>−2=<i>c</i><sup><i>p</i></sup>

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Perfect powers expressible as sums of two cubes

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On the integers represented by <i>x</i><sup>4</sup> − <i>y</i><sup>4</sup>

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ON A CLASS OF GENERALIZED FERMAT EQUATIONS

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A REFINED MODULAR APPROACH TO THE DIOPHANTINE EQUATION x<sup>2</sup> + y<sup>2n</sup> = z<sup>3</sup>

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Perfect powers expressible as sums of two fifth or seventh powers

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Rigid local systems, Hilbert modular forms, and Fermat's last theorem

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On the Equations <i>z<sup>m</sup> </i> = <i>F</i> (<i>x, y</i> ) and <i>Ax<sup>p</sup> </i> + <i>By<sup>q</sup> </i> = <i>Cz<sup>r</sup> </i>

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Fermat-type equations of signature \((13,13,p)\) via Hilbert cuspforms

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The Fermat-type equations $x^5 + y^5 = 2z^p$ or $3z^p$ solved through $\mathbb {Q}$-curves

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Solving Fermat-type equations via modular ℚ-curves over polyquadratic fields

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A complete solution to X2 + Y3 + Z5 = 0

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Galois representations attached to Q-curves and the generalized Fermat equation A 4 + B 2 = C p

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Sur les équations x<sup>p</sup>+2<sup>β</sup>y<sup>p</sup>= z<sup>2</sup>et x<sup>p</sup>+2<sup>β</sup>y<sup>p</sup>= 2z<sup>2</sup>

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Sur les courbes hyperelliptiques cyclotomiques et les équations x<sup>p</sup>-y<sup>p</sup>=cz<sup>2</sup>

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Quelques résultats sur les équations <i>ax<sup>p</sup></i> + <i>by<sup>p</sup></i> = <i>cz<sup>2</sup></i>

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The Fermat equation over \(\mathbb Q(\sqrt 2)\)

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Majorations Effectives Pour L’ Équation de Fermat Généralisée

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Sur l'équation a<sup>3</sup>+ b<sup>3</sup>= c<sup>p</sup>

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On the equation \(x^p+y^q=z^r\): a survey

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On generalized Fermat equations of signature (p,p,3)

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Rational isogenies of prime degree. (With an appendix by D. Goldfeld)

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Arithmetic of elliptic curves and diophantine equations

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Twists of \(X(7)\) and primitive solutions to \(x^2+y^3=z^7\)

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On modular representations of \(\text{Gal}(\overline{\mathbb Q}/\mathbb Q)\) arising from modular forms

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Galois properties of points of finite order of elliptic curves

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Explicit Chabauty over number fields

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Partial descent on hyperelliptic curves and the generalized Fermat equation <i>x</i> <sup>3</sup> +<i>y</i> <sup>4</sup> +<i>z</i> <sup>5</sup> =0

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Ring-theoretic properties of certain Hecke algebras

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Modular elliptic curves and Fermat's Last Theorem

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full work available at URL

https://doi.org/10.1142/s179304211530001x

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Identifiers

zbMATH Open document ID

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10.1142/S179304211530001X

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Mathematics Subject Classification ID

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zbMATH DE Number

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Sitelinks

Mathematics(1 entry)

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