Generalized Fermat equations: A miscellany

DOI10.1142/S179304211530001XzbMath1390.11065OpenAlexW1974492627MaRDI QIDQ2941067

Imin Chen, Sander R. Dahmen, Michael A. Bennett, Soroosh Yazdani

Publication date: 21 January 2015

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

Full work available at URL: https://doi.org/10.1142/s179304211530001x

zbMATH Keywords

Galois representationsFermat equations\(\mathbb{Q}\)-curvesmulti-frey techniques

Mathematics Subject Classification ID

Rational points (14G05) Elliptic curves over global fields (11G05) Exponential Diophantine equations (11D61) Higher degree equations; Fermat's equation (11D41)

Related Items (17)

On the exceptional solutions of Jeśmanowicz' conjecture ⋮ A modular approach to the generalized Ramanujan-Nagell equation ⋮ On some generalized Fermat equations of the form x2+y2n=zp$x^2+y^{2n} = z^p$ ⋮ Elliptic curves and modularity ⋮ A note on the solution to the generalized Ramanujan-Nagell equation \(x^2+(4c)^y=(c+1)^z\) ⋮ Reverse engineered Diophantine equations over \(\mathbb{Q}\) ⋮ Stability of certain higher degree polynomials ⋮ Fermat’s Last Theorem over and ⋮ On the Diophantine equation \(X^{2N}+2^{2\alpha}5^{2\beta}p^{2\gamma}=Z^5\) ⋮ Cubic forms, powers of primes and classification of elliptic curves ⋮ On the generalized Fermat equation $a^2+3b^6=c^n$ ⋮ Superelliptic equations arising from sums of consecutive powers ⋮ Elliptic curves over real quadratic fields are modular ⋮ The Generalized Fermat Equation ⋮ On a class of generalized Fermat equations of signature \((2,2n,3)\) ⋮ Recipes to Fermat-type equations of the form \(x^r + y^r =Cz^p\) ⋮ Criteria for irreducibility of mod \(p\) representations of Frey curves

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