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A note on $ 4/n=1/x+1/y+1/z$


Author: Xun Qian Yang
Journal: Proc. Amer. Math. Soc. 85 (1982), 496-498
MSC: Primary 10B20
DOI: https://doi.org/10.1090/S0002-9939-1982-0660589-3
MathSciNet review: 660589
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Abstract: Denoting by $ S(N)$ the number of natural numbers $ n$ less than $ N$ for which

$\displaystyle \frac{4} {n} = \frac{1} {x} + \frac{1} {y} + \frac{1} {z}$

has no solutions in positive integers, we show that $ S(N) \ll N/{\log ^2}N$.

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DOI: https://doi.org/10.1090/S0002-9939-1982-0660589-3
Article copyright: © Copyright 1982 American Mathematical Society