On the solutions of a parametric family of cubic Thue equations (Q839956)
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scientific article; zbMATH DE number 5601764
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On the solutions of a parametric family of cubic Thue equations |
scientific article; zbMATH DE number 5601764 |
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On the solutions of a parametric family of cubic Thue equations (English)
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4 September 2009
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The author considers the following parametric family of Thue equations \[ X^3-n(n^2+n+3)X^2Y-(n^3+2n^2+3n+3)XY^2-Y^3=\pm 1, \] with \(n\geq 0\). In particular he proves that the only solutions are \((X,Y)=\pm (1,0),\pm (0,1)\) for \(n\geq 1\). In case of \(n=0\) he finds eight further solutions.
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parametric Thue equations
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cubic equations
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Baker's method
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