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

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- by Xun Qian Yang PDF
- Proc. Amer. Math. Soc.
**85**(1982), 496-498 Request permission

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

- L. J. Mordell,
*Diophantine equations*, Pure and Applied Mathematics, Vol. 30, Academic Press, London-New York, 1969. MR**0249355**
Chao Ko, Chi Sun and S. J. Chang, - Ralph W. Jollensten,
*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), Congressus Numerantium, No. XVII, Utilitas Math., Winnipeg, Man., 1976, pp. 351–364. 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 10.1090/S0002-9939-1970-0256984-9 - H. Halberstam and H.-E. Richert,
*Sieve methods*, London Mathematical Society Monographs, No. 4, Academic Press [Harcourt Brace Jovanovich, Publishers], London-New York, 1974. MR**0424730**

*On the equation*$4/n = 1/x + 1/y + 1/z$, J. Sichuan Univ. (Science)

**3**(1964).

## Additional Information

- © Copyright 1982 American Mathematical Society
- 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