Integer solutions of the system of equations \(x^2-6y^2=1\) and \(y^2-Dz^2=4\) (Q2743115)
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scientific article; zbMATH DE number 1651088
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Integer solutions of the system of equations \(x^2-6y^2=1\) and \(y^2-Dz^2=4\) |
scientific article; zbMATH DE number 1651088 |
Statements
24 September 2001
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pair of quadratic Diophantine equations
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simultaneous Pell equations
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0.90347517
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Integer solutions of the system of equations \(x^2-6y^2=1\) and \(y^2-Dz^2=4\) (English)
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Let \(D\) be a square free positive integer. The author proves that (1) if \(D\) is an odd prime with \(D\neq 11\), then the simultaneous Pell equations \((*)\) \(x^2-6y^2=1\) and \(y^2-Dz^2=4\) have no positive integer solution \((x,y,z)\). (ii) If \(D=11\), then \((*)\) has only the solution \((x,y,z)= (49,20,6)\).
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