Coefficients and Catalan Numbers
نویسندگان
چکیده
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 P p a −1 k=0`2k k+d´mod p 2 for a −1 k=0`2k k+δ´mod p 3 for δ = 0, 1. We also show that 1 C n p a −1 X k=0 C p a n+k ≡ 1 − 3(n + 1) " p a − 1 3 « (mod p 2) for every n = 0, 1, 2,. .. , where C m is the Catalan number`2m m ´ /(m + 1), and (· 3) is the Legendre symbol.
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