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 | References | Similar Articles | Additional Information

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 $S(N) \ll N/{\log ^2}N$.

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*A note on the Egyptian problem*, Proceedings of the Seventh Southeastern Conference on Combinatorics, Graph Theory, and Computing (Louisiana State Univ., Baton Rouge, La., 1976), Utilitas Math., Winnipeg, Man., 1976, pp. 351–364. Congressus Numerantium, No. XVII. MR**0429735** - William A. Webb,
*On $4/n=1/x+1/y+1/z$*, Proc. Amer. Math. Soc.**25**(1970), 578–584. MR**256984**, DOI https://doi.org/10.1090/S0002-9939-1970-0256984-9 - H. Halberstam and H.-E. Richert,
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*On the equation*$4/n = 1/x + 1/y + 1/z$, J. Sichuan Univ. (Science)

**3**(1964).

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Article copyright:
© Copyright 1982
American Mathematical Society