Proof of Sun's Conjecture on the Divisibility of Certain Binomial Sums

On Divisibility concerning Binomial Coefficients

Binomial coefficients arise naturally in combinatorics. Recently the speaker initiated the study of certain divisibility properties of binomial coefficients, and products or sums of binomial coefficients. In this talk we introduce the speaker’s related results and various conjectures. The materials come from the author’s two preprints: 1. Z. W. Sun, Products and sums divisible by central binomi...

ON MODALITY AND DIVISIBILITY OF POISSON AND BINOMIAL MIXTURES

Some structural aspects of mixtures, in general, have been previously investigated by the author in [I] and [2]. The aim of this article is to investigate some important structural properties of the special cases of Poisson and binomial mixtures in detail. Some necessary and sufficient conditions are arrived at for different modality and divisibility properties of a Poisson mixture based o...

Divisibility Properties of a Class of Binomial Sums

We study congruence and divisibility properties of a class of combinatorial sums that involve products of powers of two binomial coefficients, and show that there is a close relationship between these sums and the theorem of Wolstenholme. We also establish congruences involving Bernoulli numbers, and finally we prove that under certain conditions the sums are divisible by all primes in specific...

A Brief Determination of Certain Class of Power Semicircle Distribution

In this paper, we give a new and direct proof for the recently proved conjecture raised in Soltani and Roozegar (2012). The conjecture can be proved in a few lines via the integral representation of the Gauss-hypergeometric function unlike the long proof in Roozegar and Soltani (2013).

Additions and Corrections "M.H.Alamatsaz- On Modality and Divisibility of Poisson and Binomial Mixtures. J.Sci. I.R. Iran, Vol.l,No.3, Spring 1990