On a Supercongruence Conjecture of Z.-***

作     者：Guo-shuai MAO Guo-shuai MAO

作者机构：Department of MathematicsNanjing University of Information Science and TechnologyNanjing 210044China 

出 版 物：《Chinese Annals of Mathematics,Series B》 (数学年刊（B辑英文版）)

年 卷 期：2022年第43卷第3期

页      面：417-424页

核心收录：

学科分类：07[理学] 0701[理学-数学] 070101[理学-基础数学] 

基　　金：supported by the National Natural Science Foundation of China(Nos.12001288 12071208) 

主　　题：Supercongruences Binomial coefficients Fermat quotient Jacobi symbol 

摘      要：In this paper,the author partly proves a supercongruence conjectured by Z.-*** in *** p be an odd prime and let a∈Z^(+).Then,if p≡1(mod 3),[5/6p^(a)]∑k=0(2kk)/16^(k)≡(3/p^(a))(mod p^(2))is obtained,where(■)is the Jacobi symbol.