On the solution of \(x^2-dy^2=\pm m\). (Q820167)
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scientific article; zbMATH DE number 5017484
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On the solution of \(x^2-dy^2=\pm m\). |
scientific article; zbMATH DE number 5017484 |
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On the solution of \(x^2-dy^2=\pm m\). (English)
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6 April 2006
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The authors study the Pellian equation \(x^ 2-dy^ 2=\pm m\). Gauss gave an efficient algorithm for solving it. The authors give an algorithm that is (in the authors' words ``essentially the same as Gauss' but a little more efficient and simpler''. Finally they propose an improvement of a factorization algorithm based on Shanks' SQUFOF method.
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quadratic Diophantine equation
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Pell equation
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continued fraction method
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prime decomposition
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0.7767269611358643
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0.7746203541755676
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