On the solutions of \(x^2 = By^p + Cz^p\) and \(2x^2 = By^p + Cz^p\) over totally real fields (Q6612383)

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scientific article; zbMATH DE number 7920317
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English
On the solutions of \(x^2 = By^p + Cz^p\) and \(2x^2 = By^p + Cz^p\) over totally real fields
scientific article; zbMATH DE number 7920317

    Statements

    On the solutions of \(x^2 = By^p + Cz^p\) and \(2x^2 = By^p + Cz^p\) over totally real fields (English)
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    30 September 2024
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    Diophantine equations
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    semi-stability
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    irreducibility of Galois representations
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    modularity of elliptic curves
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    level lowering
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