A supercongruence conjecture of Rodriguez-Villegas for a certain truncated hypergeometric function Original Research Article

Fernando Rodriguez-Villegas has been studying hypergeometric families of Calabi–Yau manifolds, and from his investigations he has found (numerically) many possible supercongruences. For example, he conjectures for every odd prime p thatimageHere, we use the theory of Gaussian hypergeometric series, the properties of the p-adic Γ-function, and a strange combinatorial identity to prove this conjecture.