Proof of a supercongruence via the Wilf–Zeilberger method

In this paper, we prove a supercongruence via the Wilf–Zeilberger method and symbolic summation algorithms in setting of difference rings. That is, for any prime p>3,∑n=0(p−1)/23n+1(−8)n(2nn)3≡p(−1p)+p34(2p)Ep−3(14)(modp4), where (⋅p) stands Legendre symbol, En(x) are Euler polynomials. This confirms special case recent conjecture Z.-W. Sun (Sun, 2019, (2.18)).