On the number of solutions of simultaneous Pell equations (Q5890440)
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scientific article; zbMATH DE number 1709923
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On the number of solutions of simultaneous Pell equations |
scientific article; zbMATH DE number 1709923 |
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On the number of solutions of simultaneous Pell equations (English)
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21 February 2002
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simultaneous quadratic Diophantine equations
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linear forms in logarithms
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Lucas sequences
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The following theorem is proved: Let \(a,b\) be fixed distinct positive integers with \(\max(a,b)\geq 1.4\times 10^{57}\); then the simultaneous Diophantine equations \(x^2-az^2= y^2-bz^2=1\) have at most two solutions \((x,y,z)\) in positive integers.
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