Preprint , arXiv : 0909 . 3808 VARIOUS CONGRUENCES INVOLVING BINOMIAL COEFFICIENTS AND HIGHER - ORDER CATALAN NUMBERS
نویسندگان
چکیده
Let p be a prime and let a be a positive integer. In this paper we investigate P p a −1 k=0`(h+1)k k+d´/m k modulo a prime p, where d and m are integers with −h < d p a and m ≡ 0 (mod p). We also study congruences involving higher-order Catalan numbers C (h) k = 1 hk+1`(h+1)k k ´ and ¯ C (h) k = h k+1`(h+1)k k ´. Our tools include linear recurrences and the theory of cubic residues. Here are some typical results in the paper. (i) If p a ≡ 1 (mod 6) then p a −1
منابع مشابه
Se p 20 09 Preprint , arXiv : 0909 . 3808 VARIOUS CONGRUENCES INVOLVING BINOMIAL COEFFICIENTS AND HIGHER - ORDER CATALAN NUMBERS
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