ON SOME NEW CONGRUENCES FOR BINOMIAL COEFFICIENTS

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Abstract
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 [ ] for d = 0, …, pa and [ ] for δ = 0, 1. We also show that [ ] for every n = 0, 1, 2, …, where Cm is the Catalan number [ ], and [ ] is the Legendre symbol.