A general p-adic WZ identity yields p^4 refinements of Van Hamme's (E.2) and (F.2) supercongruences and of two Swisher supercongruences, with Euler-polynomial corrections.
$p$-adic analogues of hypergeometric identities and their applications
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In this paper, we confirm several conjectures posed by Sun recently; for example, we prove that for any odd prime $p$ we have $$ \sum_{k=0}^{p-1}A_k\equiv\begin{cases}4x^2-2p\pmod{p^2}\quad&\text{if $p=x^2+2y^2\ (x,y\in\mathbb{Z})$},\\ 0\pmod{p^2}\quad&\text{if $p\equiv5,7\pmod{8}$},\end{cases} $$ where $A_n:=\sum_{k=0}^n\binom{n+k}{k}^2\binom{n}{k}^2$ are the Ap\'{e}ry numbers.
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Refinements of Van Hamme's (E.2) and (F.2) supercongruences and two supercongruences by Swisher
A general p-adic WZ identity yields p^4 refinements of Van Hamme's (E.2) and (F.2) supercongruences and of two Swisher supercongruences, with Euler-polynomial corrections.