On the number of solutions of Σi=111 1/xi=1 in distinct odd natural numbers

被引：5

作者：

Arce-Nazario, R. ^{[1
]}

Castro, E. ^{[2
]}

Figueroa, R. ^{[2
]}

机构：

[1] Univ Puerto Rico, Dept Comp Sci, San Juan, PR 00936 USA

[2] Univ Puerto Rico, Dept Math, San Juan, PR 00936 USA

来源：

JOURNAL OF NUMBER THEORY | 2013年 / 133卷 / 06期

关键词：

Egyptian fractions; DIOPHANTINE EQUATION; FRACTIONS; INTEGERS;

D O I：

10.1016/j.jnt.2012.11.011

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this paper we computed all the 379118 solutions of the equation Sigma(k)(i=1) 1/x(i) = 1 in distinct odd natural numbers for k = 11. We provide a lower bound for the number of solutions of Sigma(13)(i=1) 1/x(i) = 1. Also, we answer similar questions about the equation Sigma(k-1)(i=1) 1/x(i) + 1/lcm(x(1), ... ,x(k-1)) Finally, we prove some results concerning optimization of x(1) and x(11). (C) 2013 Elsevier Inc. All rights reserved.

引用

页码：2036 / 2046

页数：11

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