论文标题
关于埃及分数数量的注释
A note on the number of Egyptian fractions
论文作者
论文摘要
精炼了对盘的估计，多布斯，弗里德兰德，hetzel和pappalardi，我们表明，对于所有$ k \ geq 2 $，整数$ 1 \ leq a \ leq a \ leq n $，以便等式$ a/n = 1/n = 1/m_1 + \ dotsc + dotsc + dotsc + dotsc + 1/m_k $ y soluty Iss $ ___________ $ n^{1-1/2^{k -2} + o（1）} $ as $ n $ to to Infinity。证明是基本的。
Refining an estimate of Croot, Dobbs, Friedlander, Hetzel and Pappalardi, we show that for all $k \geq 2$, the number of integers $1 \leq a \leq n$ such that the equation $a/n = 1/m_1 + \dotsc + 1/m_k$ has a solution in positive integers $m_1, \dotsc, m_k$ is bounded above by $n^{1 - 1/2^{k-2} + o(1)}$ as $n$ goes to infinity. The proof is elementary.
