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《山东大学学报(理学版)》 ›› 2025, Vol. 60 ›› Issue (5): 93-99.doi: 10.6040/j.issn.1671-9352.0.2023.287

• • 上一篇    

一类含Catalan数的超同余式

杨继真1,2,王云鹏3*   

  1. 1.上海师范大学数理学院, 上海 200234;2.洛阳师范学院数学科学学院, 河南 洛阳 471934;3.洛阳理工学院数学与物理教学部, 河南 洛阳 471023
  • 发布日期:2025-05-19
  • 通讯作者: 王云鹏(1981— ),男,讲师,博士,研究方向为组合数学. E-mail:yunpengwang1981@163.com
  • 作者简介:杨继真(1984— ),女,副教授,硕士,研究方向为组合数学. E-mail:yangjizhen116@163.com*通信作者:王云鹏(1981— ),男,讲师,博士,研究方向为组合数学. E-mail:yunpengwang1981@163.com
  • 基金资助:
    国家自然科学基金资助项目(12271234);河南省青年骨干教师计划资助项目(2020GGJS194);河南省一流本科课程《组合数学》(豫教[2020]13099号)

Some super congruences involving Catalan numbers

YANG Jizhen1,2, WANG Yunpeng3*   

  1. 1. Department of Mathematics, Shanghai Normal University, Shanghai 200234, China;
    2. Department of Mathematics, Luoyang Normal College, Luoyang 471934, Henan, China;
    3. Department of Mathematics and Physics, Luoyang Institute of Science and Technology, Luoyang 471023, Henan, China
  • Published:2025-05-19

摘要: 以广义调和数为桥梁,利用级数变换等方法建立若干含有中心二项式系数、Catalan数及Bernoulli数的同余式,并推广了一些已有结果。

关键词: 中心二项式系数, Catalan数, Bernoulli数, 同余式

Abstract: Using the generalized harmonic number and the method of series transformation, some super congruences involving central binomial coefficient, Catalan number and Bernoulli number are established, and some known results are generalized.

Key words: central binomial coefficient, Catalan number, Bernoulli number, congruences

中图分类号: 

  • O157.1
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