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 m_1 , . . . , m_k such that a/n=1/m_1+ ··· +1/m_ k . Let A k (n) be the number of solutions a to this equation. In this article, we give a formula for A 2 (p) and a parametrization for Egyptian fractions of length 3, which allows us to give bounds to A 3 (n), to f a (n) = #{(m 1 , m 2 , m 3 ) : a/n=1/m_1+ ··· +1/m_ k}, and finally to F (n) = #{(a, m 1 , m 2 , m 3 ) : a/n=a/n=1/m_1+ ··· +1/m_ k}.

Luca, F., Banderier, C., Alexis Gomez Ruiz, C., Pappalardi, F., Treviño, E. (2021). ON EGYPTIAN FRACTIONS OF LENGTH 3. REVISTA DE LA UNION MATEMATICA ARGENTINA, 62(1), 257-274 [10.33044/REVUMA.1798].

ON EGYPTIAN FRACTIONS OF LENGTH 3

Abstract

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 m_1 , . . . , m_k such that a/n=1/m_1+ ··· +1/m_ k . Let A k (n) be the number of solutions a to this equation. In this article, we give a formula for A 2 (p) and a parametrization for Egyptian fractions of length 3, which allows us to give bounds to A 3 (n), to f a (n) = #{(m 1 , m 2 , m 3 ) : a/n=1/m_1+ ··· +1/m_ k}, and finally to F (n) = #{(a, m 1 , m 2 , m 3 ) : a/n=a/n=1/m_1+ ··· +1/m_ k}.
Scheda breve Scheda completa Scheda completa (DC)
2021
Luca, F., Banderier, C., Alexis Gomez Ruiz, C., Pappalardi, F., Treviño, E. (2021). ON EGYPTIAN FRACTIONS OF LENGTH 3. REVISTA DE LA UNION MATEMATICA ARGENTINA, 62(1), 257-274 [10.33044/REVUMA.1798].
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Utilizza questo identificativo per citare o creare un link a questo documento: `https://hdl.handle.net/11590/361566`
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