A parametric family of quartic Thue equations (Q2773328)
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scientific article; zbMATH DE number 1709919
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | A parametric family of quartic Thue equations |
scientific article; zbMATH DE number 1709919 |
Statements
A parametric family of quartic Thue equations (English)
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21 February 2002
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quartic Thue equation
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simultaneous Pellian equations
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linear forms in logarithms
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0.9661479
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0.96592224
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0.94901454
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0.9447595
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0.93918794
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0.9364727
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0.9249368
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The authors consider the Diophantine equation NEWLINE\[NEWLINEx^4 - 4cx^3y + (6c + 2) x^2 y^2 + 4cxy^3 + y^4 = 1,NEWLINE\]NEWLINE and prove that, for \(c \geq 3\) an integer, it has no solution except the trivial ones: \((\pm 1, 0)\), \((0, \pm 1)\). The authors apply a method of Tzanakis, which reduces the problem to a system of Pellian equations.
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