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

DOI10.1023/A:1009835521324zbMath0939.11016OpenAlexW2912599154MaRDI QIDQ1124970

Alain Kraus

Publication date: 2 July 2000

Published in: The Ramanujan Journal (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1023/a:1009835521324

zbMATH Keywords

Galois representationsmodular representationsgeneralized Fermat equation

Mathematics Subject Classification ID

Elliptic curves over global fields (11G05) Higher degree equations; Fermat's equation (11D41)

Related Items (10)

Selmer groups as flat cohomology groups ⋮ Lecture on the abc Conjecture and Some of Its Consequences ⋮ The equation \(x^{2n}+y^{2n}=z^5\) ⋮ Fermat-type equations of signature \((13,13,p)\) via Hilbert cuspforms ⋮ Generalized Fermat equations: A miscellany ⋮ Homogeneous forms of degree 3 and \(p\)-th powers ⋮ On the irreducibility of the iterates of 𝑥ⁿ-𝑏 ⋮ On the equation $s^2+y^{2p} = \alpha^3$ ⋮ Perfect powers expressible as sums of two cubes ⋮ Recipes to Fermat-type equations of the form \(x^r + y^r =Cz^p\)

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