ON SOME NEW CONGRUENCES FOR BINOMIAL COEFFICIENTS

Author:

SUN ZHI-WEI1,TAURASO ROBERTO2

Affiliation:

1. Department of Mathematics, Nanjing University, Nanjing 210093, P. R. China

2. Dipartimento di Matematica, Università di Roma "Tor Vergata", Roma 00133, Italy

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.

Publisher

World Scientific Pub Co Pte Lt

Subject

Algebra and Number Theory

Reference9 articles.

1. A. Granville, Organic Mathematics, CMS Conference Proceedings 20 (Amer. Math. Soc., Providence, RI, 1997) pp. 253–276.

2. On Wolstenholme's theorem and its converse

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