The Solutions of Diophantine Equation \frac{1^4}{v_1^4}+\frac{2^4}{v_2^4}+\frac{3^4}{v_3^4}+...+\frac{k^4}{v_k^4}=1
Article Sidebar
Main Article Content
Abstract
In this paper, we introduce solutions of the Diophantine equation on the following from:
where are positive integer such that
and
. The results show that there will be only 1 solution when
, there will be only 3 solutions when
, and there will be at least 4 partial solutions when
.
Article Details
This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.
References
Thamkaew, P., Kameeh, P., Maneelek, P., and Wongmookham, S. (2019). Solutions of the Diophantine equation (1) frac{1}{x_1}+frac{3}{x^{_{2}}}+frac{5}{x_3}+...+frac{2k-1}{x_k}=1 and (2) . frac{2}{x_1}+frac{4}{x^{_{2}}}+frac{6}{x_3}+...+frac{2k}{x_k}=1 Sakthong: Journal of Science and Technology (STTT). Vol. 6, No. 1, pp. 1-10
Burshtein, N. (2017). On solution of the Diophantine equation, frac{1}{x_1}+frac{2}{x^{_{2}}}+frac{3}{x_3}+...+frac{k}{x_k}=1 are integers and k = x1 when 2leq {x_{1}}< {x_{2}}< {x_{3}}< ...
Thamkaew, P. and Thamkaew, J. (2022). Solutions of the Diophantine Equation frac{1^4}{v_1}+frac{2^4}{v_2}+frac{3^4}{v_3}+...+frac{k^4}{v_k}=1. Science and Technology Nakhon Sawan Rajabhat University Journal. Vol. 14, Issue 20, pp. 128-126