Some divisibility properties of binomial coefficients
نویسندگان
چکیده
منابع مشابه
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...
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Recently, Z. Sun proved that 2 (2m + 1) ( 2m m ) | ( 6m 3m )( 3m m ) for m ∈ Z>0. In this paper, we consider a generalization of this result by defining bn,k = 2k (n + 2k − 2)!! (n− 2)!! k! . In this notation, Sun’s result may be expressed as 2 (2m + 1) | b(2m+1),(2m+1)−1 for m ∈ Z>0. In this paper, we prove that 2n | bn,un±2r for n ∈ Z>0 and u, r ∈ Z>0 with un ± 2r > 0. In addition, we prove a...
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ژورنال
عنوان ژورنال: Journal of Number Theory
سال: 2018
ISSN: 0022-314X
DOI: 10.1016/j.jnt.2017.08.005