ON SOME NEW CONGRUENCES FOR BINOMIAL COEFFICIENTS

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.