On a problem of Erdös (Q1355082)
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scientific article; zbMATH DE number 1011049
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On a problem of Erdös |
scientific article; zbMATH DE number 1011049 |
Statements
On a problem of Erdös (English)
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3 December 1997
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A generalized version of a problem of P. Erdös is solved in the paper. If \(1< a_1< \cdots <a_s\) are positive integers and \(\sum^s_{i=1} a_i^{-1}<n\) then this sum cannot split into \(n\) parts in such a manner that all partial sums are \(\leq 1\). If \(\sum^s_{i=1} a_i^{-1} <n (1-e^{1-n})\) then the mentioned decomposition is possible.
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sums of inverses of integers
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decomposition
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partial sums
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