上的克朗克尔数集

IF 0.6 4区数学 Q3 MATHEMATICS

Bulletin of the Australian Mathematical Society Pub Date : 2024-03-08 DOI:10.1017/s0004972724000133

SAYAN GOSWAMI, WEN HUANG, XIAOSHENG WU

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引用次数: 0

摘要

如果一个偶数正数可以写成两个素数之差，那么它就是麦列数；如果一个偶数正数可以用无限多种方法写成两个素数之差，那么它就是克罗内克数。一般认为，所有偶数都是克罗内克数。我们研究了克罗内克数的除法和乘法，并证明这些数相当丰富。我们证明了存在一个可计算常数 k 和一个由最多 720 个可计算的麦列特数组成的集合 D，对于任意整数 n，$kn$ 都可以表示为 D 中的一个克罗内克数和一个麦列特数的乘积。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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ON THE SET OF KRONECKER NUMBERS

A positive even number is said to be a Maillet number if it can be written as the difference between two primes, and a Kronecker number if it can be written in infinitely many ways as the difference between two primes. It is believed that all even numbers are Kronecker numbers. We study the division and multiplication of Kronecker numbers and show that these numbers are rather abundant. We prove that there is a computable constant k and a set D consisting of at most 720 computable Maillet numbers such that, for any integer n,

$kn$

can be expressed as a product of a Kronecker number and a Maillet number in D. We also prove that every positive rational number can be written as a ratio of two Kronecker numbers.

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来源期刊

Bulletin of the Australian Mathematical Society 数学-数学

CiteScore

1.20

自引率

14.30%

发文量

149

审稿时长

4-8 weeks

期刊介绍： Bulletin of the Australian Mathematical Society aims at quick publication of original research in all branches of mathematics. Papers are accepted only after peer review but editorial decisions on acceptance or otherwise are taken quickly, normally within a month of receipt of the paper. The Bulletin concentrates on presenting new and interesting results in a clear and attractive way. Published Bi-monthly Published for the Australian Mathematical Society