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We prove some 3-adic congruences for binomial sums, which were conjectured by Zhi-Wei Sun. For example, for any integer m  1 (mod 3) and any positive integer n, we have (Formula presented.) where 3(n) denotes the 3-adic order of n. In our proofs, we use several auxiliary combinatorial identities and a series converging to 0 over the 3-adic field. ? 2013 Science China Press and Springer-Verlag Berlin Heidelberg.

Some 3-adic congruences for binomial sums