Various congruences involving binomial coefficients and higher-order Catalan numbers

Details Various congruences involving binomial coefficients and higher-order Catalan numbers Various congruences involving binomial coefficients and higher-order Catalan numbers

2009-09-21

arxiv.org/abs/0909.3808v2

Mathematics

Number Theory

33 pages. Extended version

Scientific paper

Let $p$ be a prime and let $a$ be a positive integer. In this paper we investigate $\sum_{k=0}^{p^a-1}\binom[(h+1)k,k+d]/m^k$ modulo a prime $p$, where $d$ and $m$ are integers with $-h

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