Results 11 to 20 of about 1,205,068 (305)

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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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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The q-Binomial Coefficient for Negative Arguments and Some q-Binomial Summation Identities [PDF]

, 2023
Using a property of the q-shifted factorial, an identity for q-binomial coefficients is proved, which is used to derive the formulas for the q-binomial coefficient for negative arguments.
Kronenburg, M. J.
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On some series involving the binomial coefficients $binom{3n}{n}$ [PDF]

Notes on Number Theory and Discrete Mathematics
Using 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, Robert Frontczak, Taras Goy   +2 more
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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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Three new classes of binomial Fibonacci sums [PDF]

Transactions on Combinatorics
In this paper, we introduce three new classes of binomial sums involving Fibonacci (Lucas) numbers and weighted binomial coefficients. One particular result is linked to a problem proposal recently published in the journal The Fibonacci Quarterly.
Robert Frontczak
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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, Thor Martinsen, Pantelimon Stanica   +2 more
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A sum of binomial coefficients [PDF]

Mathematics of Computation, 1978
An explicit expression is derived for the sum of the ( k + 1 ) (k + 1) st binomial coefficients in the nth, ( n − m ) (n - m) th, ( n − 2 m ) (n - 2m) th,... row of the arithmetic triangle.
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On the divisibility of binomial coefficients

Ars Mathematica Contemporanea, 2020
In Pacific J. Math. 292 (2018), 223-238, Shareshian and Woodroofe asked if for every positive integer $n$ there exist primes $p$ and $q$ such that, for all integers $k$ with $1 \leq k \leq n-1$, the binomial coefficient $\binom{n}{k}$ is divisible by at least one of $p$ or $q$. We give conditions under which a number $n$ has this property and discuss a
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