On the resolution of the equations \(U_n=\binom x3\) and \(V_n=\binom x3\) (Q2785022)
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scientific article; zbMATH DE number 1733234
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On the resolution of the equations \(U_n=\binom x3\) and \(V_n=\binom x3\) |
scientific article; zbMATH DE number 1733234 |
Statements
1 October 2002
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recurrence sequences
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binomial coefficients
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Fibonacci sequence
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Lucas sequence
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Pell sequence
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elliptic equations
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On the resolution of the equations \(U_n=\binom x3\) and \(V_n=\binom x3\) (English)
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It is proved that there are only finitely many binomial coefficients of the form \(\binom{x}{3}\) in certain binary recurrences. A simple method for the determination of these coefficients in the sequences is also given. The author illustrates the method by the Fibonacci, Lucas and Pell sequences. The proofs ultimately rely on the theory and practical resolution of elliptic equations.
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