Proof of some conjectural hypergeometric supercongruences via curious identities

Abstract In this paper, we prove several supercongruences conjectured by Z.-W. Sun ten years ago via certain strange hypergeometric identities. For example, for any prime p > 3 , we show that ∑ k = 0 p − 1 ( 4 k 2 k + 1 ) ( 2 k k ) 48 k ≡ 0 ( mod p 2 ) , and ∑ k = 0 p − 1 ( 2 k k ) ( 3 k k ) 24 k ≡ { ( ( 2 p − 2 ) / 3 ( p − 1 ) / 3 ) ( mod p 2 ) if p ≡ 1 ( mod 3 ) , p / ( ( 2 p + 2 ) / 3 ( p + 1 ) / 3 ) ( mod p 2 ) if p ≡ 2 ( mod 3 ) . We also obtain some other results of such types.