A practical number is a positive integer n such that every positive integer less than n can be written as a sum of distinct divisors of n. We prove that most of the binomial coefficients are practical numbers. Precisely, letting f(n) denote the number of binomial coefficients (nk), with 0≤k≤n, that are not practical numbers, we show that f(n
Abstract. In 1947 Fine obtained an expression for the number ap(n) of bi-nomial coefficients on row ...
This paper discusses the real and complex numbers of binomial coefficients in combinatorial geometri...
Summary. The article focuses on simple identities found for binomials, their divisibility, and basic...
A practical number is a positive integer n such that every positive integer less than n can be writt...
A positive integer n is practical if every m \u3c= n a can be written as a sum of distinct divisors ...
. A positive integer m is said to be practical if every integer n 2 (1; m) is a sum of distinct posi...
A positive integer m is said to be a practical number if every integer n, with 1≤n≤∂(m), is a sum of...
AbstractA positive integermis said to be a practical number if every integern, with 1⩽n⩽σ(m), is a s...
1 A positive integer m is a practical number if every positive integer n < m is a sum of distinct...
A positive integer m is a practical number if every positive integer n is a sum of distinct divisor...
This paper presents a theorem for computing a binomial coefficient with positive real number. This i...
AbstractA counting argument is developed and divisibility properties of the binomial coefficients ar...
The primary goal of this paper is to achieve a simple generalization on binomial coefficients for al...
© 2017 In this paper, we deal with the problem of bisecting binomial coefficients. We find many (pre...
In this note we present an explicit formula for the partial sum of binomial coefficients, where both...
Abstract. In 1947 Fine obtained an expression for the number ap(n) of bi-nomial coefficients on row ...
This paper discusses the real and complex numbers of binomial coefficients in combinatorial geometri...
Summary. The article focuses on simple identities found for binomials, their divisibility, and basic...
A practical number is a positive integer n such that every positive integer less than n can be writt...
A positive integer n is practical if every m \u3c= n a can be written as a sum of distinct divisors ...
. A positive integer m is said to be practical if every integer n 2 (1; m) is a sum of distinct posi...
A positive integer m is said to be a practical number if every integer n, with 1≤n≤∂(m), is a sum of...
AbstractA positive integermis said to be a practical number if every integern, with 1⩽n⩽σ(m), is a s...
1 A positive integer m is a practical number if every positive integer n < m is a sum of distinct...
A positive integer m is a practical number if every positive integer n is a sum of distinct divisor...
This paper presents a theorem for computing a binomial coefficient with positive real number. This i...
AbstractA counting argument is developed and divisibility properties of the binomial coefficients ar...
The primary goal of this paper is to achieve a simple generalization on binomial coefficients for al...
© 2017 In this paper, we deal with the problem of bisecting binomial coefficients. We find many (pre...
In this note we present an explicit formula for the partial sum of binomial coefficients, where both...
Abstract. In 1947 Fine obtained an expression for the number ap(n) of bi-nomial coefficients on row ...
This paper discusses the real and complex numbers of binomial coefficients in combinatorial geometri...
Summary. The article focuses on simple identities found for binomials, their divisibility, and basic...
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