In this paper we establish some new congruences involving central binomial coefficients as well as Catalan numbers. Let p be a prime and let a be any positive integer. We determine [Formula: see text] for d = 0, …, p a and [Formula: see text] for δ = 0, 1. We also show that [Formula: see text] for every n = 0, 1, 2, …, where C m is the Catalan number [Formula: see text], and [Formula: see text] is the Legendre symbol.
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Sun et al. (2011) studied this question.