Length and denominators of Egyptian fractions. III (Q749575)
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scientific article; zbMATH DE number 4173082
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Length and denominators of Egyptian fractions. III |
scientific article; zbMATH DE number 4173082 |
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Length and denominators of Egyptian fractions. III (English)
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1990
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[For parts I, II cf. the second author, ibid. 28, 258-271 and 272-282 (1988; Zbl 0637.10006 and Zbl 0637.10007).] The authors prove that for large N every rational number \(a/N\in]0,1[\) has an Egyptian fraction expansion \(a/N=\sum^{r}_{j=1}1/n_ j,\) where \(r\leq (1+o(1))\log N/\log_ 2N\) and \(n_ r\leq 4N \log^ 2N \log_ 2N.\) This is essentially best possible.
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Egyptian fraction expansion
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