Results 1 to 10 of about 174,940 (323)
Binomial-coefficient multiples of irrationals [PDF]
Monatshefte f�r Mathematik, 1998 Denote by $x$ a random infinite path in the graph of Pascal's triangle (left and right turns are selected independently with fixed probabilities) and by $d_n(x)$ the binomial coefficient at the $n$'th level along the path $x$. Then for a dense $G_{\delta}
Adams, Terrence M., Petersen, Karl E.
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Perfect numbers, Wieferich primes and the solutions of \binom{2n}{n} ≡ 2ⁿ mod n [PDF]
Notes on Number Theory and Discrete Mathematics, 2023 In this article we focus on the solutions of a congruence equation: "\binom{2n}{n} ≡ 2ⁿ mod n". Using the main result of this article and the SageMath software, we improve largely the number of known solutions.
Gabriel Guedes, Ricardo Machado
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New combinatorial proof of the multiple binomial coefficient identity
Vojnotehnički Glasnik, 2022 Introduction/purpose: In this paper a new combinatorial proof of an already existing multiple sum with multiple binomial coefficients is given. The derived identity is related to the Fibonacci numbers. Methods: Combinatorial reasoning is used to obtain
Vuk N. Stojiljković
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An upper bound on binomial coefficients in the de Moivre – Laplace form
Журнал Белорусского государственного университета: Математика, информатика, 2022 We provide an upper bound on binomial coefficients that holds over the entire parameter range an whose form repeats the form of the de Moivre – Laplace approximation of the symmetric binomial distribution.
Sergey V. Agievich
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Reciprocal Formulae among Pell and Lucas Polynomials
Mathematics, 2022 Motivated by a problem proposed by Seiffert a quarter of century ago, we explicitly evaluate binomial sums with Pell and Lucas polynomials as weight functions.
Mei Bai, Wenchang Chu, Dongwei Guo
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Binomial Sum Relations Involving Fibonacci and Lucas Numbers
AppliedMath, 2023 In this paper, we provide a first systematic treatment of binomial sum relations involving (generalized) Fibonacci and Lucas numbers. The paper introduces various classes of relations involving (generalized) Fibonacci and Lucas numbers and different ...
Kunle Adegoke +2 more
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Generalized double Fibonomial numbers
Ratio Mathematica, 2021 From the beginning of 20th century, generalization of binomial coefficient has been deliberated broadly. One of the most famous generalized binomial coefficients are Fibonomial coefficients, obtained by substituting Fibonacci numbers in place of natural ...
Mansi Shah, Shah Devbhadra
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Supercongruences involving Apéry-like numbers and binomial coefficients
AIMS Mathematics, 2022 Let $ \{S_n\} $ be the Apéry-like sequence given by $ S_n = \sum_{k = 0}^n\binom nk\binom{2k}k\binom{2n-2k}{n-k} $. We show that for any odd prime $ p $, $ \sum_{n = 1}^{p-1}\frac {nS_n}{8^n}{\equiv} (1-(-1)^{\frac{p-1}2})p^2\ (\text{ mod}\ {p^3}) $. Let
Zhi-Hong Sun
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Poset binomials and rainbow characters [PDF]
Discrete Mathematics & Theoretical Computer Science, 2013 This paper introduces a variation on the binomial coefficient that depends on a poset and interpolates between $q$-binomials and 1-binomials: a total order gives the usual $q$-binomial, and a poset with no relations gives the usual binomial coefficient ...
Daniel Bragg, Nathaniel Thiem
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Generating Functions for Four Classes of Triple Binomial Sums
Mathematics, 2022 By means of the generating function approach, four classes of triple sums involving circular products of binomial coefficients are investigated. Recurrence relations and rational generating functions are established.
Marta Na Chen, Wenchang Chu
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