Wolstenholme定理关于模p的8次幂的研究  

Study on the 8th Power of Module p by Wolstenholme Theorem

作　　者：闫少强 杨萍 郑万里 吴丰轩 YAN Shao-qiang;YANG Ping;ZHENG Wan-li;WU Feng-xuan(Foundation Department,Rocket Army Engineering University,Xi'an 710025,China)

机构地区：[1]火箭军工程大学基础部,陕西西安710025

出　　处：《数学的实践与认识》2022年第10期200-205,共6页Mathematics in Practice and Theory

摘　　要：著名的Wolstenholme定理,它断言了在任意的素数p≥5下二项式系数的同余性质.在前人的基础上对此进一步推广,运用了MESTROVIó对于p的7次幂的研究及其证明方法,证明了在对于任意的素数p≥11的条件下模p的8次幂的相关简式,对Wolstenholme定理进行了推广.the famous Wolstenholme theorem asserts the congruence property of binomial coefficients under any prime number p≥5.On the basis of predecessors,this paper further generalizes this,uses MESTROVI s research on the 7th power of module p and its proof method,proves the relevant simple formula of the 8th power of module p under the condition of arbitrary prime number p≥11,and generalizes Wolstenholme's theorem.

关 键 词：WOLSTENHOLME定理 二项式系数 同余 Wolstenholme定理的推广 

分 类 号：O157[理学—数学]