Proof of Some Conjectural Congruences of Z.-W. Sun

摘要

In this paper, we confirm some conjectural congruences of Sun. For example, we prove that for any odd prime p we have where Dn denotes the nth Domb number and qp(2) denotes the Fermat quotient (2p-1 - 1)/p. This confirms a conjecture of Sun Sci. China Math. 54 (2011),2509-2535.