A polynomial variant of a problem of Diophantus and Euler (Q1430421)
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scientific article; zbMATH DE number 2067051
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | A polynomial variant of a problem of Diophantus and Euler |
scientific article; zbMATH DE number 2067051 |
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A polynomial variant of a problem of Diophantus and Euler (English)
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27 May 2004
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It is shown that there are no polynomials \(f_1(X),\dots,f_4(X)\) with integral coefficients having the property that the polynomials \(f_if_j-1\) are squares for \(1\leq i<j\leq 4\). The main point of the proof consists in showing that two polynomial binary linear recurrences, resulting from consideration of a system of two polynomial Pell equations, do not have common elements.
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polynomial diophantine equations
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problem of Diophantos
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binary linear recurrence
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0.97449565
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0.93444324
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0.9285953
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0.91288424
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0.9046173
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0.8975859
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0.8964429
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