有移码质数分母的单位分数

IF 1.3 3区 数学 Q1 MATHEMATICS
Thomas F. Bloom
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引用次数: 0

摘要

我们证明任何有理正数都是分母在 $\{p-1 : p\textrm { prime}\}$ 中的不同单位分数之和。对于在 \mathbb {Z}\backslash \{0\}$中的任何$h,只要满足必要的全等条件,集合$\{p-h : p\textrm { prime}\}$ 也有同样的结论。我们还证明,只要满足必要的全等条件,这对于任何相对正密度的素数子集都是正确的。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Unit fractions with shifted prime denominators

We prove that any positive rational number is the sum of distinct unit fractions with denominators in $\{p-1 : p\textrm { prime}\}$. The same conclusion holds for the set $\{p-h : p\textrm { prime}\}$ for any $h\in \mathbb {Z}\backslash \{0\}$, provided a necessary congruence condition is satisfied. We also prove that this is true for any subset of the primes of relative positive density, provided a necessary congruence condition is satisfied.

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来源期刊
CiteScore
3.00
自引率
0.00%
发文量
72
审稿时长
6-12 weeks
期刊介绍: A flagship publication of The Royal Society of Edinburgh, Proceedings A is a prestigious, general mathematics journal publishing peer-reviewed papers of international standard across the whole spectrum of mathematics, but with the emphasis on applied analysis and differential equations. An international journal, publishing six issues per year, Proceedings A has been publishing the highest-quality mathematical research since 1884. Recent issues have included a wealth of key contributors and considered research papers.
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