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We study two-term Egyptian fraction representations of a given rational number. We consider the case of m/n where each prime factor p of n satisfies p ≡ ±1 (mod m): necessary and sufficient conditions for the existence of proper two-term Egyptian fraction expressions of such m/n are given, together with methods to find these representations. Furthermore, we determine the number of proper two-term Egyptian fraction expressions for 1/m, 2/m, 3/m, 4/m and 6/m.
- Egyptian fractions
- Unit fraction
- Diophantine equation
- Bartoš, P. A remark on the number of solutions of the equation 1/x + 1/y = a/b in natural numbers, Časopis Pešt. Mat. Vol. 95, 1970, 411–415.
- Gay, R., C. Shute, The Rhind Mathematical Papyrus: an Ancient Egyptian Text, British Museum Press, London, 1987.
- Guy Richard K. Unsolved problems in number theory, 3rd ed., New York: Springer-Verlag, 2004.
- Rav, Y. On the representation of rational numbers as a sum of a fixed number of unit fractions, J. Reine Angew. Math. Vol. 222, 1966, 207–213.
Cite this paperAPA
Chen, T., & Koo, R. (2013). Two-term Egyptian fractions. Notes on Number Theory and Discrete Mathematics, 19(2), 15-25.Chicago
Chen, Tieling, and Reginald Koo. “Two-term Egyptian Fractions.” Notes on Number Theory and Discrete Mathematics 19, no. 2 (2013): 15-25.MLA
Chen, Tieling, and Reginald Koo. “Two-term Egyptian Fractions.” Notes on Number Theory and Discrete Mathematics 19.2 (2013): 15-25. Print.