On distinct unit fractions whose sum equals 1 (Q5921599)
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scientific article; zbMATH DE number 3411125
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On distinct unit fractions whose sum equals 1 |
scientific article; zbMATH DE number 3411125 |
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On distinct unit fractions whose sum equals 1 (English)
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1973
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It is shown that the Diophantine equation \[ \frac 1{x_1}+\frac 1{x_2}+ \dots+\frac 1{x_k}=1 \] is solvable with distinct naturals \(x_1<x_2<\dots<x_k\) satisfying the following conditions, namely (i) \(x_i\) are odd for \(i=1,2,\dots,k\), (ii) \(x_i\nmid x_j\) for \(i\neq j\). The solutions are obtained without the help of a computer.
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