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On a question of Erdös and Graham
被引：0
作者：
I. E. Shparlinski
机构：
[1] Department of Computing,
[2] Macquarie University,undefined
[3] Sydney,undefined
[4] NSW 2109,undefined
[5] Australia¶ email: igor@ics.mq.edu.au,undefined
来源：
Archiv der Mathematik
|
2002年
/
78卷
关键词：
Positive Answer;
Distinct Integer;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
We prove that for any \documentclass[12pt]{minimal}
\usepackage{amsmath}
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\begin{document}
$ \varepsilon > 0 $\end{document} there is \documentclass[12pt]{minimal}
\usepackage{amsmath}
\usepackage{wasysym}
\usepackage{amsfonts}
\usepackage{amssymb}
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\begin{document}
$ k (\varepsilon) $\end{document} such that for any prime p and any integer c there exist \documentclass[12pt]{minimal}
\usepackage{amsmath}
\usepackage{wasysym}
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\begin{document}
$ k \leqq k(\varepsilon) $\end{document} pairwise distinct integers xi with \documentclass[12pt]{minimal}
\usepackage{amsmath}
\usepackage{wasysym}
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\begin{document}
$ 1 \leqq x_{i} \leqq p^{\varepsilon}, i = 1, \ldots, k $\end{document}, and such that¶¶\documentclass[12pt]{minimal}
\usepackage{amsmath}
\usepackage{wasysym}
\usepackage{amsfonts}
\usepackage{amssymb}
\usepackage{amsbsy}
\usepackage{mathrsfs}
\usepackage{upgreek}
\setlength{\oddsidemargin}{-69pt}
\begin{document}
$ \sum\limits_{i=1}^k {{1}\over{x_i}} \equiv c\quad (\mathrm{mod}\, p). $\end{document}¶¶ This gives a positive answer to a question of Erdös and Graham.
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页码：445 / 448
页数：3
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