共 1 条
- [1] Chen Y.G.(2009)Eight consecutive positive odd numbers none of which can be expressed as a sum of two prime powers Bull. Aust. Math. Soc., 80 237-243
On integers 2(p + ia) not of the form ak+ϕ(m)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${a^k + \phi(m)}$$\end{document}
被引：0
作者：
X.-G. Sun
机构：
[1] School of Sciences,HuaiHai Institute of Technology
关键词：
power of ;
the Euler totient function;
prime;
Selberg’s sieve method;
11A07;
11B25;
11P32;
D O I：
10.1007/s10474-015-0524-7
中图分类号：
学科分类号：
摘要：
Let a≧2\documentclass[12pt]{minimal}
\usepackage{amsmath}
\usepackage{wasysym}
\usepackage{amsfonts}
\usepackage{amssymb}
\usepackage{amsbsy}
\usepackage{mathrsfs}
\usepackage{upgreek}
\setlength{\oddsidemargin}{-69pt}
\begin{document}$${a \geqq 2}$$\end{document} be an even integer and let L≧1\documentclass[12pt]{minimal}
\usepackage{amsmath}
\usepackage{wasysym}
\usepackage{amsfonts}
\usepackage{amssymb}
\usepackage{amsbsy}
\usepackage{mathrsfs}
\usepackage{upgreek}
\setlength{\oddsidemargin}{-69pt}
\begin{document}$${L \geqq 1}$$\end{document} be an integer. We show that for a sufficiently large x, the number of primes p≦x\documentclass[12pt]{minimal}
\usepackage{amsmath}
\usepackage{wasysym}
\usepackage{amsfonts}
\usepackage{amssymb}
\usepackage{amsbsy}
\usepackage{mathrsfs}
\usepackage{upgreek}
\setlength{\oddsidemargin}{-69pt}
\begin{document}$${p \leqq x}$$\end{document} such that 2p + 2a, . . . , 2p + 2La can not be expressed as ak+ϕ(m)\documentclass[12pt]{minimal}
\usepackage{amsmath}
\usepackage{wasysym}
\usepackage{amsfonts}
\usepackage{amssymb}
\usepackage{amsbsy}
\usepackage{mathrsfs}
\usepackage{upgreek}
\setlength{\oddsidemargin}{-69pt}
\begin{document}$${a^{k} +\phi(m)}$$\end{document} is at least C(a,L)xlogx\documentclass[12pt]{minimal}
\usepackage{amsmath}
\usepackage{wasysym}
\usepackage{amsfonts}
\usepackage{amssymb}
\usepackage{amsbsy}
\usepackage{mathrsfs}
\usepackage{upgreek}
\setlength{\oddsidemargin}{-69pt}
\begin{document}$${C(a,L) \frac{x}{log x}}$$\end{document}, where k, m are positive integers, ϕ(m)\documentclass[12pt]{minimal}
\usepackage{amsmath}
\usepackage{wasysym}
\usepackage{amsfonts}
\usepackage{amssymb}
\usepackage{amsbsy}
\usepackage{mathrsfs}
\usepackage{upgreek}
\setlength{\oddsidemargin}{-69pt}
\begin{document}$${\phi(m)}$$\end{document} is the Euler totient function and the constant C(a, L) depends on a, L.
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页码：332 / 340
页数：8
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