Multi-Frey \(\mathbb Q\)-curves and the Diophantine equation \(a^2+b^6=c^n\) (Q442451)
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scientific article; zbMATH DE number 6064727
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Multi-Frey \(\mathbb Q\)-curves and the Diophantine equation \(a^2+b^6=c^n\) |
scientific article; zbMATH DE number 6064727 |
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Multi-Frey \(\mathbb Q\)-curves and the Diophantine equation \(a^2+b^6=c^n\) (English)
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10 August 2012
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The authors prove that, for any integer \(n\geq 3\), the Diophantine equation \(a^2+b^6=c^n\) has no nontrivial positive integer solutions with \(a\) and \(b\) coprime. The proof draws on the theory of Galois representations and modular forms, extending the techniques used to prove Fermat's last theorem and subsequent variants. The authors generalize to \(\mathbb{Q}\)-curves the multi-Frey technique developed by Siksek.
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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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