Results 11 to 20 of about 165,625 (255)
Practical central binomial coefficients [PDF]
Quaestiones Mathematicae, 2020 A practical number is a positive integer n such that all positive integers less than n can be written as a sum of distinct divisors of n. Leonetti and Sanna proved that, as x → +∞, the central binomial coefficient is a practical number for all positive ...
C. Sanna
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Factors of certain sums involving central q-binomial coefficients [PDF]
Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas, 2021 Recently, Ni and Pan proved a $q$-congruence on certain sums involving central $q$-binomial coefficients, which was conjectured by Guo. In this paper, we give a generalization of this $q$-congruence and confirm another $q$-congruence, also conjectured by Guo.
Guo, Victor J. W., Wang, Su-Dan
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On certain congruences involving central binomial coefficients
Mathematica Montisnigri, 2023 Let p be an odd prime. In this paper, using some properties of Fibonacci numbers, reciprocal polynomials for Fibonacci polynomials, and Legendre symbol, we establish some congruences involving central binomial coefficient modulo p and p^2.
Rachid Boumahdi +2 more
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Symmetry, 2021 We prove some finite sum identities involving reciprocals of the binomial and central binomial coefficients, as well as harmonic, Fibonacci and Lucas numbers, some of which recover previously known results, while the others are new.
Necdet Batır, A. Sofo
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New congruences for central binomial coefficients
Advances in Applied Mathematics, 2009 Let p be a prime and let a be a positive integer. In this paper we determine $\sum_{k=0}^{p^a-1}\binom{2k}{k+d}/m^k$ and $\sum_{k=1}^{p-1}\binom{2k}{k+d}/(km^{k-1})$ modulo $p$ for all d=0,...,p^a, where m is any integer not divisible by p.
Sun, Zhi-Wei, Tauraso, Roberto
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Some congruences involving central q-binomial coefficients
Advances in Applied Mathematics, 2010 16 pages, detailed proofs of Theorems 4.1 and 4.3 are added, to appear in Adv.
Guo, Victor J. W., Zeng, Jiang
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Two permutation classes enumerated by the central binomial coefficients [PDF]
, 2013 We define a map between the set of permutations that avoid either the four patterns $3214,3241,4213,4231$ or $3124,3142,4123,4132$, and the set of Dyck prefixes.
Barnabei, Marilena +2 more
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On congruences related to central binomial coefficients
Journal of Number Theory, 2011 It is known that $\sum_{k=0}^\infty\binom{2k}{k}/((2k+1)4^k)= /2$ and $\sum_{k=0}^\infty\binom{2k}{k}/((2k+1)16^k)= /3$. In this paper we obtain their p-adic analogues such as $$\sum_{p/23 is a prime and E_0,E_1,E_2,... are Euler numbers. Besides these, we also deduce some other congruences related to central binomial coefficients.
Zhi-Wei Sun
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More congruences for central binomial coefficients
Journal of Number Theory, 2010 Let \(p>5\) be a prime number. The author proves that \[ \sum_{k=1}^{p-1}\frac{1}{k^2}\binom{2k}{k}^{-1}\equiv\frac13 \frac{H(1)}{p}\pmod {p^3} \] and that \[ \sum_{k=1}^{p-1}\frac{(-1)^k}{k^3}\binom{2k}{k}^{-1}\equiv-\frac25 \frac{H(1)}{p^2}\pmod {p^3}, \] where \(H(1)=\sum_{k=1}^{p-1}\frac{1}{k}\).
Roberto Tauraso
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INTEGRAL REPRESENTATIONS AND INEQUALITIES OF EXTENDED CENTRAL BINOMIAL COEFFICIENTS [PDF]
, 2021 In the paper, the author presents three integral representations of extended central binomial coefficient, proves decreasing and increasing properties of two power-exponential functions involving extended (central) binomial coefficients, derives several ...
Chunfu Wei
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