Halfway to a solution of \(x^ 2 - Dy^ 2 = -3\) (Q1805365)
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scientific article; zbMATH DE number 754101
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Halfway to a solution of \(x^ 2 - Dy^ 2 = -3\) |
scientific article; zbMATH DE number 754101 |
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Halfway to a solution of \(x^ 2 - Dy^ 2 = -3\) (English)
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11 May 1995
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It is well known that the continued fraction expansion of \(\sqrt {D}\) readily displays the midpoint of the principal cycle of ideals; i.e., the point halfway to a solution of \(x^ 2- Dy^ 2= \pm1\). Here it is analogously noted that the point halfway to a solution of \(x^ 2- Dy^ 2= -3\) can be recognized. There are lengthy, but not complicated, procedures about the exact calculations.
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quadratic diophantine equations
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quadratic extensions
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continued fraction expansion
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principal cycle of ideals
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exact calculations
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