Results 11 to 20 of about 55,236 (313)
On Binomial Coefficient Residues [PDF]
Canadian Journal of Mathematics, 1957 The number of binomial coefficients , which are congruent to j , 0 ≤ j ≤ p − 1, modulo the prime number p is denoted by θj(n). In this paper we give systems of simultaneous linear difference equations with constant coefficients whose
J . B. Roberts
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Inequalities for Binomial Coefficients
Journal of Mathematical Analysis and Applications, 1999 For any real number \(r\) with \(r>1\), let \(c_r= (2\pi(1-{1\over r}))^{-1/2}\) and \(d_r= (r-1)/(1-{1\over r})^r\). Let \(B_{2m}\) \((m= 1,2,\dots)\) be the Bernoulli numbers defined by \[ {z\over e^z-1}=1-{z\over 2}+\sum^\infty_{m=1} B_{2m}{z^{2m}\over (2m)!}.
Sasvári, Zoltán
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Sum of Successive Partitions of Binomial Coefficient
, 2022 This paper focuses on the successive partition method applied to a binomial coefficient in combinatorial geometric series. The coefficient for each term in combinatorial geometric series refers to a binomial coefficient.
Chinnaraji Annamalai
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Ascending and Descending Orders of Annamalai’s Binomial Coefficient
, 2022 This paper presents the analysis of ascending and descending orders with Annamalai’s binomial coefficient compared with traditional combination of combinatorics.
Chinnaraji Annamalai
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Theorem on the Binomial Coefficient for Positive Real Number
, 2023 This paper presents a theorem for computing a binomial coefficient with positive real number.
Chinnaraji Annamalai
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On some series involving the binomial coefficients $binom{3n}{n}$ [PDF]
Notes on Number Theory and Discrete MathematicsUsing a simple transformation, we obtain much simpler forms for some series involving binomial coefficients $binom{3n}{n}$ derived by Necdet Batir. New evaluations are given and connections with Fibonacci numbers and the golden ratio are established ...
Kunle Adegoke +2 more
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Successive Partition Method for Binomial Coefficient in Combinatorial Geometric Series
, 2022 This paper focuses on the successive partition method applied to a binomial coefficient in combinatorial geometric series. The coefficient for each term in combinatorial geometric series refers to a binomial coefficient.
Chinnaraji Annamalai
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q-Analogue of a binomial coefficient congruence
International Journal of Mathematics and Mathematical Sciences, 1995 We establish a q-analogue of the congruence (papb)≡(ab) (modp2) where p is a prime and a and b are positive integers.
W. Edwin Clark
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Bisecting binomial coefficients
Discrete Applied Mathematics, 2017 In this paper, we deal with the problem of bisecting binomial coefficients. We find many (previously unknown) infinite classes of integers which admit nontrivial bisections, and a class with only trivial bisections. As a byproduct of this last construction, we show conjectures Q2 and Q4 of Cusick and Li.
Eugen J. Ionascu +2 more
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ON DIVISIBILITY OF BINOMIAL COEFFICIENTS [PDF]
Journal of the Australian Mathematical Society, 2012 AbstractIn this paper, motivated by Catalan numbers and higher-order Catalan numbers, we study factors of products of at most two binomial coefficients.
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