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World Scientific Publishing, International Journal of Number Theory, 03(07), p. 645-662

DOI: 10.1142/s1793042111004393

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On some new congruences for binomial coefficients

Journal article published in 2007 by Zhi-Wei Sun, Roberto Tauraso
This paper is available in a repository.
This paper is available in a repository.

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