EGYPTIAN FRACTIONS WITH ODD DENOMINATORS

被引：2

作者：

Elsholtz, Christian ^{[1
]}

机构：

[1] Graz Univ Technol, Inst Anal & Zahlentheorie, Kopernikusgasse 24, A-8010 Graz, Austria

来源：

QUARTERLY JOURNAL OF MATHEMATICS | 2016年 / 67卷 / 03期

关键词：

NUMBER; REPRESENTATIONS;

D O I：

10.1093/qmath/haw020

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

The number of solutions of the diophantine equation Sigma(k)(i=1) 1/x(i) = 1, in particular when the xi are distinct odd positive integers is investigated. The number of solutions S(k) in this case is, for odd k: exp(exp(c(1) k/logk)) <= S(k) <= exp(exp(c(2)k)) with some positive constants c(1) and c(2). This improves upon an earlier lower bound of S)k) >= exp((1 + o(1)) (log 2/2)k(2)).

引用

收藏

页码：425 / 430

页数：6

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