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

Main Article Content

Kulprapa Srimud
Nonthiya Makate
Tawan Ampawa
Tadbun Jantree

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 Nov. 15];12(1):11-6. Available from: https://ph02.tci-thaijo.org/index.php/past/article/view/246172
Section
Mathematics and Applied Statistics

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.