On the Diophantine Equation 2/x+3/y+4/z=1/2

Article Sidebar

PDF
Published: Apr 22, 2022
DOI: https://doi.org/10.14456/past.2022.2
Keywords:
Diophantine equation

Main Article Content

Kulprapa Srimud
Department of Mathematics, Faculty of Science and Technology, Rajamangala University of Technology Thanyaburi
Nonthiya Makate
Department of Mathematics, Faculty of Science and Technology, Rajamangala University of Technology Thanyaburi
Tawan Ampawa
Department of Mathematics, Faculty of Science and Technology, Rajamangala University of Technology Thanyaburi
Tadbun Jantree
Department of Mathematics, Faculty of Science and Technology, Rajamangala University of Technology Thanyaburi

Abstract

In this paper, we find all solutions of the Diophantine equation  gif.latex?\frac{2}{x}+\frac{3}{y}+\frac{4}{z}=\frac{1}{2}  where  gif.latex?x , gif.latex?y and  gif.latex?z are positive integers.

Article Details

How to Cite
1.
Srimud K, Makate N, Ampawa T, Jantree T. On the Diophantine Equation 2/x+3/y+4/z=1/2. Prog Appl Sci Tech. [Internet]. 2022 Apr. 22 [cited 2024 Dec. 17];12(1):11-6. Available from: https://ph02.tci-thaijo.org/index.php/past/article/view/246172
Issue
Vol. 12 No. 1 (2022): January - April 2022
Section
Mathematics and Applied Statistics
Creative Commons License

This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Crossref
Scopus
Google Scholar
Europe PMC

References

Elsholtz C. Sum of k Unit Fractions. Transactions of the American Mathematical Society. 2001; 353(8): 3209-3227.

Li D.L. Equation 4/n=1/x+1/y+1/z. Journal of Number Theory. 1981; 13(4): 485-494.

Rabago J.F.T.,Tagle R.P. On the Area and volume of a certain regular solid and the Diophantine Equation 1/2=1/x+1/y+1/z. Notes on Number Theory and Discrete Mathematics. 2013; 19(3): 28-32.

Pakapongpun A. Integral Solutions of the Diophantine Equation 1/x+2/y+3/z=1/2. Mathematical Journal. 2019; 64(699): 36-43.

Sandor J. A note on a Diophantine equation. Notes on Number Theory and Discrete Mathematics. 2013; 19(4): 1-3.

Webb W.A. On 4/n=1/x+1/y+1/z. Proceedings of American Mathematical Society. 1970; 25(3): 578-584.