C. Banderier, Carlos Alexis Gómez Ruiz, F. Luca, F. Pappalardi, Enrique Treviño
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Let a, n be positive integers that are relatively prime. We say that a/n can be represented as an Egyptian fraction of length k if there exist positive integers m1, . . . ,mk such that a n = 1 m1 + · · ·+ 1 mk . Let Ak(n) be the number of solutions a to this equation. In this article, we give a formula for A2(p) and a parametrization for Egyptian fractions of length 3, which allows us to give bounds to A3(n), to fa(n) = #{(m1,m2,m3) : a n = 1 m1 + 1 m2 + 1 m3 }, and finally to F (n) = #{(a,m1,m2,m3) : a n = 1 m1 + 1 m2 + 1 m3 }.
期刊介绍:
Revista de la Unión Matemática Argentina is an open access journal, free of charge for both authors and readers. We publish original research articles in all areas of pure and applied mathematics.