Add to ORKGAbstract. Let a, n be positive integers. In this paper we prove that n I (an- a)[n /2]! For any positive integer a and n, Smarandache [3] proved that (1) n I (an- a)(n- 1)!' The above division relation is the Smarandache divisibility theorem (see [1, Notions 126]). In this paper we give an improvement on (1) as follows: Theorem. F or any positive integers a and n, we have (2) n I (an- a) [ n / 2]!, where [n / 2] is the largest integer which does not exceed n / 2. Proof. The division relation (2) holds for n ~ 9, we may assume that n> 9. By Fermat's theorem (see [ 2, Theorem 71]), if n is a prime, then we have (3) n I (an- a), 152 for an
Smarandache's function may be defined as follows: S(n) = the smallest positive integer such that S(n...
The Smarandache function S:N * ~N * is defined [9] by the condition that S(n) is the smallest positi...
The Smarandache-Coman function is the function defined on the set of non-null positive integers with...
Abstract Let a,n be positive integers. In this paper we prove that S(a)S(c1).. • S(d') ~n!(S(a)...
The Smarandache Function is defined as Sen) = k. Where k is the smallest integer such that n divide...
in [1 J. Our aim is to shmv that certain results from om recent paper [3] can be obtained in a simpl...
For a positive integer n. the Smarandache function S(n) is defined as the smallest positive integer ...
Smarandache's function is defined thus: S( n) = is the smallest integer such that S( n)! is divisib...
positive integer. This arithmetical function is connected to the number of divisors of n, and other ...
Abstract For any positive integer n, the famous F.Smarandache function S(n) is defined as the smalle...
For a given positive integer n, we consider positive integers a(1), a(2)... at such that a(1) !a(2)!...
Abstract For any positive integer n, the famous F.Smarandache function S(n) is defined as the smalle...
Smarandache's function is defined thus: S ( n) = is the smallest integer such that S ( n)! is ...
A sequence of rational integers g is called a divisibility sequence if and only if n | m ⇒ g(n) | g...
Abstract For any positive integer n ≥ 1, the Smarandache quotients Q(n) is defined as the smallest p...
Smarandache's function may be defined as follows: S(n) = the smallest positive integer such that S(n...
The Smarandache function S:N * ~N * is defined [9] by the condition that S(n) is the smallest positi...
The Smarandache-Coman function is the function defined on the set of non-null positive integers with...
Abstract Let a,n be positive integers. In this paper we prove that S(a)S(c1).. • S(d') ~n!(S(a)...
The Smarandache Function is defined as Sen) = k. Where k is the smallest integer such that n divide...
in [1 J. Our aim is to shmv that certain results from om recent paper [3] can be obtained in a simpl...
For a positive integer n. the Smarandache function S(n) is defined as the smallest positive integer ...
Smarandache's function is defined thus: S( n) = is the smallest integer such that S( n)! is divisib...
positive integer. This arithmetical function is connected to the number of divisors of n, and other ...
Abstract For any positive integer n, the famous F.Smarandache function S(n) is defined as the smalle...
For a given positive integer n, we consider positive integers a(1), a(2)... at such that a(1) !a(2)!...
Abstract For any positive integer n, the famous F.Smarandache function S(n) is defined as the smalle...
Smarandache's function is defined thus: S ( n) = is the smallest integer such that S ( n)! is ...
A sequence of rational integers g is called a divisibility sequence if and only if n | m ⇒ g(n) | g...
Abstract For any positive integer n ≥ 1, the Smarandache quotients Q(n) is defined as the smallest p...
Smarandache's function may be defined as follows: S(n) = the smallest positive integer such that S(n...
The Smarandache function S:N * ~N * is defined [9] by the condition that S(n) is the smallest positi...
The Smarandache-Coman function is the function defined on the set of non-null positive integers with...