A parametric congruence motivated by Orr's identity

Chen Wang, Zhi-Wei Sun

For any $m,n\in \mathbb{N}=\{0,1,2\dots \}$, the truncated hypergeometric series ${}_{m+1}{F}_m$ is defined by $$ {}_{m+1}F_m\bigg[\begin{matrix}x_0&x_1&\ldots&x_m\\ &y_1&\ldots&y_m\e…