Factors of sums of powers of binomial coefficients
نویسندگان
چکیده
We prove divisibility properties for sums of powers of binomial coefficients and of q-binomial coefficients. Dedicated to the memory of Paul Erdős
منابع مشابه
On the Order of Lacunary Sums of Binomial Coefficients
In this paper we study the exact orders of lacunary sums of binomial coefficients. It is remarkable that the periodic patterns evolving from powers of 2 differ markedly from those of other prime powers. For the latter ones the pattern is transparent and is determined by the first term. For the former ones multisected generating functions are used to obtain the exact order or lower bounds on it.
متن کاملBernstein Basis Functions Related to Combinatorial Sums Involving Binomial Coefficients and Special Numbers
By using generating functions, which contained alternative forms, we derive identities, some new and old, for the Bernstein basis functions. Integrating these identities, we also derive combinatorial sums involving binomial coefficients. We give relations between these combinatorial sums and generating functions for special numbers, we investigate relations related to finite sums of the powers ...
متن کاملSome Identities involving the Partial Sum of q-Binomial Coefficients
We give some identities involving sums of powers of the partial sum of q-binomial coefficients, which are q-analogues of Hirschhorn’s identities [Discrete Math. 159 (1996), 273–278] and Zhang’s identity [Discrete Math. 196 (1999), 291–298].
متن کاملDivisibility 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...
متن کاملFactors of alternating sums of products of binomial and q-binomial coefficients
In this paper we study the factors of some alternating sums of products of binomial and q-binomial coefficients. We prove that for all positive integers
متن کامل