A note on $4/n=1/x+1/y+1/z$
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- by Xun Qian Yang
- Proc. Amer. Math. Soc. 85 (1982), 496-498
- DOI: https://doi.org/10.1090/S0002-9939-1982-0660589-3
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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 $S(N) \ll N/{\log ^2}N$.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, On the equation $4/n = 1/x + 1/y + 1/z$, J. Sichuan Univ. (Science) 3 (1964).
- 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
Bibliographic 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