Sur l'équation \(x^5 + y^5 = z^5\) (Q771182)
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scientific article; zbMATH DE number 3143758
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Sur l'équation \(x^5 + y^5 = z^5\) |
scientific article; zbMATH DE number 3143758 |
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Sur l'équation \(x^5 + y^5 = z^5\) (English)
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1958
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From a general theorem of Kummer, it follows that the equation \(x^5 + y^5 = z^5\) \((xyz \neq 0)\) is insoluble in the field \(K(\sqrt 5)\). A simple proof of this fact is given, using descent on the number of prime factors of \(z\) in the equation \(x^5 - y^5 = E (\sqrt 5)^{5+\mu} z^5\), where \(E\) is a unit of \(K(\sqrt 5)\).
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quintic Diophantine equations
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