An arithmetic conjecture on an arctangent sum (Q2874378)
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scientific article; zbMATH DE number 6252051
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | An arithmetic conjecture on an arctangent sum |
scientific article; zbMATH DE number 6252051 |
Statements
30 January 2014
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arctangent
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recurrence
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valuations
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An arithmetic conjecture on an arctangent sum (English)
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There is a conjecture that the recursively defined sequence \(x_1=1\), \(x_n=\frac{n+x_{n-1}}{1-nx_{n-1}}\) has no integer terms for \(n\geq 5\). The paper shows that the subsequences \(x_{19n+5}\) and \(x_{19n+13}\) contain no integer values.
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