AbstractIt is known that for sufficiently large n and m and any r the binomial coefficient (nm) which is close to the middle coefficient is divisible by pr where p is a ‘large’ prime. We prove the exact divisibility of (nm) by pr for p > c(n). The lower bound is essentially the best possible. We also prove some other results on divisibility of binomial coefficients
AbstractTwo results are obtained about P(n), the largest prime factor of an integer n. The average v...
AbstractWe investigate lower bounds for ω((sn)) − ω((rn)) that are independent of n. This difference...
AbstractWe prove that for any integer d multinomial coefficients satisfying some conditions are exac...
AbstractThe following two facts are shown: 1.(i) There is a computable constant γ > 0 such that, giv...
AbstractThe Lucas theorem for binomial coefficients implies some interesting tensor product properti...
We prove that [Formula Omitted] thus dealing with open problems concerning divisors of binomial coef...
AbstractWe prove that for any integer d multinomial coefficients satisfying some conditions are exac...
AbstractGiven a positive integer l, this paper establishes the existence of constants η > 1 and δ > ...
Let A be the set of all positive integers n such that n divides the central binomial coefficient (2n...
Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/46612/1/222_2005_Article_BF01388495.pd
AbstractIn 1878 Lucas established a method of computing binomial coefficients modulo a prime. We est...
We obtain a lower bound for the minimum over positive integers such that the sum of certain powers o...
Let σ(n) denote the sum of divisors function, and let ϒ be Euler’s constant. We prove that if there ...
Let σ(n) denote the sum of divisors function, and let ϒ be Euler’s constant. We prove that if there ...
Let σ(n) denote the sum of divisors function, and let ϒ be Euler’s constant. We prove that if there ...
AbstractTwo results are obtained about P(n), the largest prime factor of an integer n. The average v...
AbstractWe investigate lower bounds for ω((sn)) − ω((rn)) that are independent of n. This difference...
AbstractWe prove that for any integer d multinomial coefficients satisfying some conditions are exac...
AbstractThe following two facts are shown: 1.(i) There is a computable constant γ > 0 such that, giv...
AbstractThe Lucas theorem for binomial coefficients implies some interesting tensor product properti...
We prove that [Formula Omitted] thus dealing with open problems concerning divisors of binomial coef...
AbstractWe prove that for any integer d multinomial coefficients satisfying some conditions are exac...
AbstractGiven a positive integer l, this paper establishes the existence of constants η > 1 and δ > ...
Let A be the set of all positive integers n such that n divides the central binomial coefficient (2n...
Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/46612/1/222_2005_Article_BF01388495.pd
AbstractIn 1878 Lucas established a method of computing binomial coefficients modulo a prime. We est...
We obtain a lower bound for the minimum over positive integers such that the sum of certain powers o...
Let σ(n) denote the sum of divisors function, and let ϒ be Euler’s constant. We prove that if there ...
Let σ(n) denote the sum of divisors function, and let ϒ be Euler’s constant. We prove that if there ...
Let σ(n) denote the sum of divisors function, and let ϒ be Euler’s constant. We prove that if there ...
AbstractTwo results are obtained about P(n), the largest prime factor of an integer n. The average v...
AbstractWe investigate lower bounds for ω((sn)) − ω((rn)) that are independent of n. This difference...
AbstractWe prove that for any integer d multinomial coefficients satisfying some conditions are exac...
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