A note on the number of Egyptian fractions

2022/10/11 by Lebowitz-Lockard, Noah, Souza, Victor
#FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.2210.07921

Abstract

Refining an estimate of Croot, Dobbs, Friedlander, Hetzel and Pappalardi, we show that for all k ≥ 2, the number of integers 1 ≤ a ≤ n such that the equation a/n = 1/m₁ + \dotsc + 1/m_k has a solution in positive integers m₁, \dotsc, m_k is bounded above by n^1 - 1/2^k-2 + o(1) as n goes to infinity. The proof is elementary.

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