A way to remove duplication from ∑Ni=1 1/xi

Tomoyuki Idogawa; Masayoshi Tsutsumi

doi:10.1006/jnth.1996.0095

A way to remove duplication from ∑^N_i=1 1/x_i

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Abstract

The main purpose of this paper is to show that we can rewrite a sum of unit fractions ∑^N_{i = 1} 1/x_i< 1 in which 0<x_i≤x_{i+ 1} to the form ∑^N_{i = 1} 1/x′_i in which 0 <x′_i<x′_{i+ 1}. In other words, it is always possible to remove duplication from ∑^N_{i = 1} 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.

Original language	English
Pages (from-to)	215-224
Number of pages	10
Journal	Journal of Number Theory
Volume	59
Issue number	2
DOIs	https://doi.org/10.1006/jnth.1996.0095
Publication status	Published - 1996 Aug
Externally published	Yes

ASJC Scopus subject areas

Algebra and Number Theory

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10.1006/jnth.1996.0095

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abstract = "The main purpose of this paper is to show that we can rewrite a sum of unit fractions ∑Ni = 1 1/xi< 1 in which 0i≤xi+ 1 to the form ∑Ni = 1 1/x′i in which 0 ii+ 1. In other words, it is always possible to remove duplication from ∑Ni = 1 1/xi, 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.",

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A way to remove duplication from ∑^N_i=1 1/x_i

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