论文标题
埃及分数不足
Underapproximation by Egyptian fractions
论文作者
论文摘要
积极整数的增加序列$（x_i）_ {i = 1}^n $是$ n $ - 埃及的埃及不足的$θ\ in（0,1] $，如果$ \ sum_ {i = 1}}^n \ frac {1}^n \ frac {1}} {x_i} $ n $ n $ n $。 $θ$。
An increasing sequence $(x_i)_{i=1}^n$ of positive integers is an $n$-term Egyptian underapproximation of $θ\in (0,1]$ if $\sum_{i=1}^n \frac{1}{x_i} < θ$. A greedy algorithm constructs an $n$-term underapproximation of $θ$. For some but not all numbers $θ$, the greedy algorithm gives a unique best $n$-term underapproximation for all $n$. An infinite set of rational numbers is constructed for which the greedy underapproximations are best, and numbers for which the greedy algorithm is not best are also studied.
