منابع مشابه
On Prime Divisors of Binomial Coefficients
This paper, using computational and theoretical methods, deals with prime divisors of binomial coefficients: Geometric distribution and number of distinct prime divisors are studied. We give a numerical result on a conjecture by Erdôs on square divisors of binomial coefficients.
متن کاملOn Sums of Binomial Coefficients
In this paper we study recurrences concerning the combinatorial sum [n r ] m = ∑ k≡r (mod m) (n k ) and the alternate sum ∑ k≡r (mod m)(−1) (n k ) , where m > 0, n > 0 and r are integers. For example, we show that if n > m−1 then b(m−1)/2c ∑ i=0 (−1) (m− 1− i i )[n− 2i r − i ]
متن کاملOn the Conditioned Binomial Coefficients
We answer a question on the conditioned binomial coefficients raised in and article of Barlotti and Pannone, thus giving an alternative proof of an extension of Frobenius’ generalization of Sylow’s theorem.
متن کاملOn 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...
متن کاملOn P,q-binomial Coefficients
In this paper, we develop the theory of a p, q-analogue of the binomial coefficients. Some properties and identities parallel to those of the usual and q-binomial coefficients will be established including the triangular, vertical, and the horizontal recurrence relations, horizontal generating function, and the orthogonality and inverse relations. The construction and derivation of these result...
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ژورنال
عنوان ژورنال: Journal of Number Theory
سال: 1985
ISSN: 0022-314X
DOI: 10.1016/0022-314x(85)90017-4