用不同幂的和表示

IF 1.2 1区数学 Q1 MATHEMATICS

Journal fur die Reine und Angewandte Mathematik Pub Date : 2021-05-27 DOI:10.1515/crelle-2021-0048

Jianya Liu, Lilu Zhao

引用次数: 5

摘要

摘要证明了所有足够大的整数n都可以表示为n=x12+x23+⋯+x1314,n=x_{1}^{2}+x_{2} +\cdots+x_{13}^{14}，其中x1，…，x13{x_{1}，\ldots,x_{13}}是正整数。这改进了当前记录，将13个变量替换为14个。

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Representation by sums of unlike powers

Abstract It is proved that all sufficiently large integers n can be represented as n=x12+x23+⋯+x1314,n=x_{1}^{2}+x_{2}^{3}+\cdots+x_{13}^{14}, where x1,…,x13{x_{1},\ldots,x_{13}} are positive integers. This improves upon the current record with fourteen variables in place of thirteen.

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来源期刊

Journal fur die Reine und Angewandte Mathematik 数学-数学

CiteScore

2.50

自引率

6.70%

发文量

审稿时长

6-12 weeks

期刊介绍： The Journal für die reine und angewandte Mathematik is the oldest mathematics periodical still in existence. Founded in 1826 by August Leopold Crelle and edited by him until his death in 1855, it soon became widely known under the name of Crelle"s Journal. In the almost 180 years of its existence, Crelle"s Journal has developed to an outstanding scholarly periodical with one of the worldwide largest circulations among mathematics journals. It belongs to the very top mathematics periodicals, as listed in ISI"s Journal Citation Report.