Proof of a supercongruence via the Wilf–Zeilberger method. (November 2021) - Mao, Guo-Shuai
Abstract: In this paper, we prove a supercongruence via the Wilf–Zeilberger method and symbolic summation algorithms in the setting of difference rings. That is, for any prime p > 3, ∑ n = 0 ( p − 1 ) / 2 3 n + 1 ( − 8 ) n ( 2 n n ) 3 ≡ p ( − 1 p ) + p 3 4 ( 2 p ) E p − 3 ( 1 4 ) ( mod p 4 ), where ( ⋅ p ) stands for the Legendre symbol, and E n ( x ) are the Euler polynomials. This confirms a special case of a recent conjecture of Z.-W. Sun (Sun, 2019, (2.18)).