A way to remove duplication from Sigma(i=1)(N) 1/x(i)

被引：0

作者：

Idogawa, T ^{[1
]}

Tsutsumi, M ^{[1
]}

机构：

[1] WASEDA UNIV,DEPT APPL PHYS,SHINJUKU KU,TOKYO 169,JAPAN

来源：

JOURNAL OF NUMBER THEORY | 1996年 / 59卷 / 02期

关键词：

D O I：

10.1006/jnth.1996.0095

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

The main purpose of this paper is to show that we can rewrite a sum of unit fractions Sigma(i=1)(N) 1/x(i)<1 in which 0<x(i) less than or equal to x(i+1) to the form Sigma(i=1)(N) 1/x(i)' in which 0<x'(i)<x'(i+1). In other words, it is always possible to remove duplication from Sigma(i=1)(N) 1/x(i), without changing its length. Moreover, using this rewriting process, we get a new algorithm for the expansion of Egyptian fractions. We state this algorithm and show some numerical results. (C) 1996 Academic Press, Inc.

引用

页码：215 / 224

页数：10