ON SOME NEW CONGRUENCES FOR BINOMIAL COEFFICIENTS

By Zhi-Wei Sun, Roberto Tauraso. 2007

80 citations recorded by the source corpus.

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

Subfields: Algebra and Number Theory, Discrete Mathematics and Combinatorics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/9a6d3b25ccab63f29d34c66c9a81396b410f9df5

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Algebra and Number Theory

1. Ji-Cai Liu
2. Zhi-Wei Sun
3. Victor J. W. Guo
4. Zhi-Hong Sun

In Discrete Mathematics and Combinatorics

1. Ji-Cai Liu
2. Zhi-Wei Sun
3. Victor J. W. Guo
4. Zhi-Hong Sun

In Statistical and Nonlinear Physics

1. Ji-Cai Liu
2. Zhi-Wei Sun

Citations in the corpus

• Binomial coefficients, Catalan numbers and Lucas quotients (2009, background): “Later Sun and R. Tauraso [ ST1 , ST2] determined P p”
• On a congruence involving $q$-Catalan numbers (2019, background): “Both Catalan numbers and central binomial coefficients satisfy many interesting congruences (see, for instance, [7, 8]).”