Proof of Two Supercongruences of Truncated Hypergeometric Series_(4)F_(3)  

作　　者：Guo Shuai MAO 

机构地区：[1]Department of Mathematics,Nanjing University of Information Science and Technology,Nanjing 210044,P.R.China

出　　处：《Acta Mathematica Sinica,English Series》2024年第4期1015-1028,共14页数学学报（英文版）

基　　金：Supported by the National Natural Science Foundation of China(Grant No.12001288)。

摘　　要：In this paper,we prove two supercongruences conjectured by Z.-W.Sun via the Wilf-Zeilberger method.One of them is,for any prime p>3,4F3[7/6 1/2 1/2 1/2 1/6 1 1]-1/8]-1/2≡p(-2/p)+p^(3)/4(2/p)Ep-3 (mod p^(4))where(·/p)stands for the Legendre symbol,and E_(n)is the n-th Euler number.

关 键 词：Supercongruence truncated hypergeometric series Wilf–Zeilberger method Euler numbers Legendre symbol 

分 类 号：O156[理学—数学]