A note on the Erdős-Straus conjecture (Q520012)
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scientific article; zbMATH DE number 6699248
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | A note on the Erdős-Straus conjecture |
scientific article; zbMATH DE number 6699248 |
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A note on the Erdős-Straus conjecture (English)
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31 March 2017
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The authors consider the Erdős-Straus equation \(\frac{c}{n}=\frac 1x+\frac 1y+\frac 1z\), where \(n,c\) are coprime positive integers. They provide a formula for the number \(f(n,c)\) of positive integral solutions \((x,y,z)\) of the equation. The conjecture of Erdős and Straus saying that \(f(n,4)\geq 1\) for all \(n\geq 2\) is proved under certain assumptions.
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Egyptian fractions
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Diophantine equation
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number of solutions
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