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In this paper we obtain their p-adic analogues such as $$\\sum_{p/2<k<p}\\binom{2k}{k}/((2k+1)4^k)=3\\sum_{p/2<k<p}\\binom{2k}{k}/((2k+1)16^k)= pE_{p-3} (mod p^2),$$ where p>3 is a prime and E_0,E_1,E_2,... are Euler numbers. Besides these, we also deduce some other congruences related to central binomial coefficients. 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