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arXiv · 1905.06151

On ternary Egyptian fractions with prime denominator

Florian Luca·Francesco Pappalardi
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Abstract

Given a positive integer $n$ we let $A_k(n)$ be the number of positive integers $a$ such that $\frac{a}{n}=\frac{1}{m_1}+\frac{1}{m_2}+\cdots+\frac{1}{m_k}$ for some $m_1,m_2,\ldots,m_k\in {\mathbb N}$. We show that $x(\log x)^3\ll \sum_{p\le x} A_3(p)\ll x(\log x)^5$ as $x\rightarrow\infty$.

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Florian Luca, Francesco Pappalardi. 2019-05-15. On ternary Egyptian fractions with prime denominator. https://arxiv.org/abs/1905.06151

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