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A Note on $\frac{4}{n} = \frac{1}{x} + \frac{1}{y} + \frac{1}{z}$

Xun Qian Yang
Proceedings of the American Mathematical Society
Vol. 85, No. 4 (Aug., 1982), pp. 496-498
DOI: 10.2307/2044050
Stable URL: http://www.jstor.org/stable/2044050
Page Count: 3
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Since scans are not currently available to screen readers, please contact JSTOR User Support for access. We'll provide a PDF copy for your screen reader.
A Note on $\frac{4}{n} = \frac{1}{x} + \frac{1}{y} + \frac{1}{z}$
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Abstract

Denoting by $S(N)$ the number of natural numbers $n$ less than $N$ for which $$\frac{4}{n} = \frac{1}{x} + \frac{1}{y} + \frac{1}{z}$$ has no solutions in positive integers, we show that $S(N) \ll N/\log^2N$.

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