On the Diophantine Equation 1/w+1/x+1/y+1/z=u/u+1
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Abstract
In 2023, Wongsanurak and Duangdai found all positive integer solutions of the Diophantine equation , when
and
are positive integers with
and
. In this work, by using an elementary approach, we solved the Diophantine equation for any positive integer
and
. The results of the research found that the Diophantine equation under the above conditions has twenty-seven positive integer solutions.
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References
Sándor, J. A note on Diophantine equation. Notes Number Theory Discrete Math. 2013;19(4):1–3.
Zhao, W., Lu, J., Wang, L. On the integral solutions of the Egyptian fraction equation a/p=1/x+1/y+1/z. AIMS Math. 2021;6(5): 4930–7.
Sándor, J., Atanassov, K. On a Diophantine equation arising in the history of mathematics. Notes Number Theory Discrete Math. 2021;27(1):70–5.
Tadee, S., Poopra, S. On the Diophantine equation 1/x+1/y+1/z=1/n. Int J Math Comput Sci. 2023;18(2):173–7.
Tadee, S. All solutions of the Diophantine equation 1/x+1/y+1/z=u/(u+2). J Appl Res Sci Technol. 2024;23(2):1–5.
Yuan, X. On the Diophantine equation 4/n=1/x+1/y+1/z. J Algebra Number Theory Appl. 2024;63(5):459–80.
Bai, T. On 1/w+1/x+1/y+1/z=1/2 and some of its generalizations. J Inequal Appl. 2018; (197)2018:1–13.
Atri, R. On the Diophantine equations 1/x+1/y+1/z=1/4 and 1/x+1/y+1/z+1/t=1/4. Int J Sci Res. 2022;11(1):573–4.
Wongsanurak, W., Duangdai, E. The natural number solutions of the Diophantine equation 1/w+1/x+1/y+1/z=u/(u+1). Acad J Sci Appl Sci. 2023;2:91–8. (in Thai)
