Add to ORKGProposed by Marian Tetiva, National College Gheorghe Rosca Codreanu, Barlad, Romallia. Let d be a square-free positive integer greater than 1. Show that there are infinitely many positive integers n such that dn2 + I divides n!
AbstractA positive integermis said to be a practical number if every integern, with 1⩽n⩽σ(m), is a s...
Abstract. The summation formula n−1∑ i=0 εii!(ik + uk) = vk + ε n−1n!Ak−1(n) (ε = ±1; k = 1, 2,...;...
We study the Diophantine system{ x1 + · · ·+ xn = a, x3 1 + · · ·+ x3n = b, where a, b ∈ Q, ab 6 =...
Proposed by Marian Tetiva, National College "Gheorghe Rosca Codreanu," Barlad, Romallia. Let d be a ...
Let n be a positive integer. We prove nn+1e−n 2π√ n − α ≤ n! < n n+1e−n2 2π√ n − β with the best ...
For any positive integer k let φ(k), σ(k), and τ(k) be the Euler function of k, the divisor sum func...
AbstractLet d(n) denote the number of positive integers dividing the positive integer n. We show tha...
Abstract. Let a, n be positive integers. In this paper we prove that n I (an- a)[n /2]! For any posi...
AbstractThe number d(n) of positive divisors of a natural number n is known to exceed infinitely oft...
In [2] and [31 the authors ask how many primes are of the Smarandache form (see [10]) xY + yX, where...
Let n be a positive integer different of 1. We define the integer sequence q(n) where q(n) is the nu...
Abstract. The D(−1)-quadruple conjecture states that there does not exist a set of four positive int...
AbstractLet m(n) be the number of ordered factorizations of n⩾1 in factors larger than 1. We prove t...
Abstract. In this paper, it has been proved that if n is an odd integer> 3 and h = 1 is the class...
AbstractLet f(n) denote the number of factorizations of the natural number n into factors larger tha...
AbstractA positive integermis said to be a practical number if every integern, with 1⩽n⩽σ(m), is a s...
Abstract. The summation formula n−1∑ i=0 εii!(ik + uk) = vk + ε n−1n!Ak−1(n) (ε = ±1; k = 1, 2,...;...
We study the Diophantine system{ x1 + · · ·+ xn = a, x3 1 + · · ·+ x3n = b, where a, b ∈ Q, ab 6 =...
Proposed by Marian Tetiva, National College "Gheorghe Rosca Codreanu," Barlad, Romallia. Let d be a ...
Let n be a positive integer. We prove nn+1e−n 2π√ n − α ≤ n! < n n+1e−n2 2π√ n − β with the best ...
For any positive integer k let φ(k), σ(k), and τ(k) be the Euler function of k, the divisor sum func...
AbstractLet d(n) denote the number of positive integers dividing the positive integer n. We show tha...
Abstract. Let a, n be positive integers. In this paper we prove that n I (an- a)[n /2]! For any posi...
AbstractThe number d(n) of positive divisors of a natural number n is known to exceed infinitely oft...
In [2] and [31 the authors ask how many primes are of the Smarandache form (see [10]) xY + yX, where...
Let n be a positive integer different of 1. We define the integer sequence q(n) where q(n) is the nu...
Abstract. The D(−1)-quadruple conjecture states that there does not exist a set of four positive int...
AbstractLet m(n) be the number of ordered factorizations of n⩾1 in factors larger than 1. We prove t...
Abstract. In this paper, it has been proved that if n is an odd integer> 3 and h = 1 is the class...
AbstractLet f(n) denote the number of factorizations of the natural number n into factors larger tha...
AbstractA positive integermis said to be a practical number if every integern, with 1⩽n⩽σ(m), is a s...
Abstract. The summation formula n−1∑ i=0 εii!(ik + uk) = vk + ε n−1n!Ak−1(n) (ε = ±1; k = 1, 2,...;...
We study the Diophantine system{ x1 + · · ·+ xn = a, x3 1 + · · ·+ x3n = b, where a, b ∈ Q, ab 6 =...