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=0p−1(4k2k+1)(2kk)48k≡0(modp2), and∑k=0p−1(2kk)(3kk)24k≡{((2p−2)/3(p−1)/3)(modp2)ifp≡1(mod3),p/((2p+2)/3(p+1)/3)(modp2)ifp≡2(mod3). We also obtain some other results of such types.
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