Solutions of the equation \(x^ m+ y^ m= z^ m\) in \(SL_ 2 \mathbb{Z}\) (Q1906580)
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scientific article; zbMATH DE number 840337
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Solutions of the equation \(x^ m+ y^ m= z^ m\) in \(SL_ 2 \mathbb{Z}\) |
scientific article; zbMATH DE number 840337 |
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Solutions of the equation \(x^ m+ y^ m= z^ m\) in \(SL_ 2 \mathbb{Z}\) (English)
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25 February 1996
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The author is looking for solutions of the Fermat equation (see the title) with unknowns \(x\), \(y\), \(z\) being integral two by two matrices of determinant 1. Solving an open problem of the reviewer, the author proves that such a solution exists if and only if \(m\) is not divisible by 3 or 4 (in the paper the answer was stated in a more complicated form). The same result is contained in a paper by \textit{A. Khazanov} [Serdica Math J. 21, 19-40 (1995; Zbl 0829.11014)].
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existence of solutions
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Fermat equation in \(2\times 2\) matrices
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