ON THE DIOPHANTINE EQUATIONS 1/a+1/b=(nq+1)/pq AND 1/a+1/b=(nq-1)/pq

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Published: Dec 21, 2023
Keywords:
Diophantine equation positive integer solution Egyptian fraction

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Suton Tadee
Department of Mathematics, Faculty of Science and Technology, Thepsatri Rajabhat University

Abstract

In this paper, we study and find all positive integer solutions of two Diophantine equations gif.latex?\frac{1}{a}+\frac{1}{b}=\frac{nq+1}{pq} and  gif.latex?\frac{1}{a}+\frac{1}{b}=\frac{nq-1}{pq}, where gif.latex?a,b,n are positive integers and gif.latex?p,q are prime numbers with gif.latex?p>nq .

Article Details

Issue
Vol. 11 No. 3 (2023): September - December
Section
Research Article

References

Clemente, F., & Fortuny, J. M. (2021). Egyptian fractions and representation registers in the construction of the fraction concept. EURASIA Journal of Mathematics, Science and Technology Education, 17(7), 1 – 17.

Johnson, J. W. (2022). A Diophantine equation with an elementary solution. The College Mathematics Journal, 53(5), 361 – 363.

Prugsapitak, S. (2023). The Egyptian fraction of the form 1/a+1/b=(q-1)/pq. International Journal of Mathematics and Computer Science, 18(4), 595 – 597.

Prugsapitak, S. (2024). Corrigendum to the Egyptian fraction of the form 1/a+1/b=(q-1)/pq. International Journal of Mathematics and Computer Science, 19(1), 237.

Mathematical Association of America. (2019). The William Lowell Putnam Mathematical Competition. Retrieved August 12, 2023 from https://www.maa.org/sites/default/files/pdf/Putnam/CompetitionArchive/2018PutnamProblems.pdf.