New congruences involving products of two binomial coefficients

被引：0
作者：
Guo-Shuai Mao
Zhi-Wei Sun
机构：
[1] Nanjing University,Department of Mathematics
来源：
The Ramanujan Journal | 2019年 / 49卷
关键词：
Central binomial coefficients; Congruences; Legendre symbol; Primary 11B65; 11B68; Secondary 05A10; 11A07;
D O I：
暂无
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学科分类号：
摘要：
Let p>3\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$p>3$$\end{document} be a prime and let a be a positive integer. We show that if [inline-graphic not available: see fulltext] or a>1\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$a>1$$\end{document}, then [graphic not available: see fulltext]with (-)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$(-)$$\end{document} the Jacobi symbol, which confirms a conjecture of Z.-W. Sun. We also establish the following new congruences: [graphic not available: see fulltext]
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页码：237 / 256
页数：19
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