AIMS Mathematics, 2017, 2(1): 111-127. doi: 10.3934/Math.2017.1.111

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On the Diophantine equation $\frac{1}{x}+\frac{1}{y}+\frac{1}{z}=\frac{1}{3p}$

School of Mathematics and Information, China West Normal University, Nanchong 637009, P.R.China

In the present paper we obtained all positive integer solutions of some diophantine equations related to unit fraction.
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1. Z. Cao, An intruduction to Diophantine equations, Haerbin Industril university Press, 400 (1989).

2. N. Franceschine, Egyptian fractions, Sonoma State Coll., 1978.

3. Z. Ke, Q. Sun, X. Zhang,On the Diophantine equatins $\frac{4}{n}=\frac{1}{x}+\frac{1}{y}+\frac{1}{z}$, J. Sichuan University (in Chinese), 3 (1964), 23-37.

4. Z. Ke, Q. Sun,Some conjecture and problem in Number Theorey, Chinese Journal of Nature (in Chinese), 7 (1979), 411-413.

5. Y. Liu,On a problem of unit fraction, J. Sichuan University (in Chinese), 2 (1984), 113-114.

6. Palama,Sull's equarione diofantea $\frac{4}{n}=\frac{1}{x}+\frac{1}{y}+\frac{1}{z}$, Boll. Union Mat. Ital, 13 (1958), 65-72.

7. Palama,Sull's equarione diofantea $\frac{4}{n}=\frac{1}{x}+\frac{1}{y}+\frac{1}{z}$, Boll. Union Mat. Ital, 14 (1959), 82-94.

8. L. A. Rosati,Sull's equarione diofantea $\frac{4}{b}=\frac{1}{x_1}+\frac{1}{x_2}+\frac{1}{x_3}$, Boll. Union Mat. Ital, 9 (1954), 59-63.

9. B.M.Stewart,Theory of numbers, Macmillan, New York, (1964), 198-207.

10. Yamamoto,On the Diophantine equatins $\frac{4}{n}=\frac{1}{x}+\frac{1}{y}+\frac{1}{z}$, K. Men. Fac. Sci. Kyushu University, Ser.A., 19 (1965), 37-47.

Copyright Info: © 2017, Jiagui Luo, et al., licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution Licese (

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