The Solution of Diophantine Equation \frac{1^3}{u_1}+\frac{1^3}{u_2}+...+\frac{k^3}{u_k}=1
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Abstract
In this paper, we describe solutions of the Diophantine equation on the following from: where
are integers. For our result, we obtain that the equation has one solution if
three solution if
and at least four general solutions if
. Moreover, there is a clear step-by-step method of proof following a mathematical process.
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References
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Thamkaew, P., Kameeh, P., Maneelek, P., & Wongmookham, S. (2019). Solutions of the Diophantine equation (1) 1/v1 + 3/v2 + 5/v3 +...+ (2k-1)/vk = 1 and (2) 2/v1 + 4/v2 + 6/v3 +...+ 2k/vk = 1 . Sakthong: Journal of Science and Technology (STTT), 6(1), 1-10. Retrieved from https://research.kpru.ac.th/journal_science/journal/26322019-07-07.pdf
Thamkaew, P., & Thamkaew, J. (2022). Solutions of the Diophantine Equation 1^2/x1 + 2^2/x2 + 3^2/x3 +...+ k^2/xk = 1. Science and Technology Nakhon Sawan Rajabhat University Journal, 14(20), 118-126. Retrieved from https://ph02.tci-thaijo.org/index.php/JSTNSRU/article/view/245601/167842