Add to ORKGLet k ≥ 2 and n ≥ 1 be integers. We denote by ∆(n, k) = n(n+ 1) · · · (n+ k − 1). For an integer ν> 1, we denote by ω(ν) and P (ν) the number of distinct prime divisors of ν and the greatest prime factor of ν
We study prime divisors of various sequences of positive integers A(n) + 1, n = 1,...,N, such that t...
In this paper, I explore the following problem: Problem. Find instances where a product of distin...
Copyright c © 2013 Rafael Jakimczuk. This is an open access article distributed under the Creative C...
Let d ≥ 1, k ≥ 2, n ≥ 1 and y ≥ 1 be integers with gcd(n, d) = 1. We write ∆ = ∆(n, d, k) = n(n+ ...
Abstract. It is shown under Schinzel’s Hypothesis that for a given ` ≥ 1, there are infinitely many...
It is shown under Schinzel's Hypothesis that for a given l≥ 1, there are infinitely many k such that...
A classical result of Sylvester [21] (see also [16], [17]), generalizing Bertrand’s Postulate, state...
Let §P^+ (n) §denote the largest prime factor of the integer §n§ and §P ^+ y (n)§ denote the largest...
We define the arithmetic function P by P (1) = 0, and P (n) = p1 + p2+ · · ·+ pk if n has the uni...
Dans cette thèse, on s'intéresse aux plus grands facteur premiers d'entiers consécutifs. Désignons p...
The Fundamental Theorem of Arithmetic is usually stated in a form emphasizing how primes enter the s...
Abstract. For positive integers n and k, it is possible to choose primes P1, P2, · · · , Pk such ...
Let φ denote the Euler function. For a fixed integer k ≠ 0, we study positive integers n for which t...
Perfect powers in products of terms in an arithmetical progression III by T. N. Shorey (Bombay) and ...
2)2()1() ( =+=+ = xdxdxd infinitely-often. （1） where)(xd represents the number of distinct prime fac...
We study prime divisors of various sequences of positive integers A(n) + 1, n = 1,...,N, such that t...
In this paper, I explore the following problem: Problem. Find instances where a product of distin...
Copyright c © 2013 Rafael Jakimczuk. This is an open access article distributed under the Creative C...
Let d ≥ 1, k ≥ 2, n ≥ 1 and y ≥ 1 be integers with gcd(n, d) = 1. We write ∆ = ∆(n, d, k) = n(n+ ...
Abstract. It is shown under Schinzel’s Hypothesis that for a given ` ≥ 1, there are infinitely many...
It is shown under Schinzel's Hypothesis that for a given l≥ 1, there are infinitely many k such that...
A classical result of Sylvester [21] (see also [16], [17]), generalizing Bertrand’s Postulate, state...
Let §P^+ (n) §denote the largest prime factor of the integer §n§ and §P ^+ y (n)§ denote the largest...
We define the arithmetic function P by P (1) = 0, and P (n) = p1 + p2+ · · ·+ pk if n has the uni...
Dans cette thèse, on s'intéresse aux plus grands facteur premiers d'entiers consécutifs. Désignons p...
The Fundamental Theorem of Arithmetic is usually stated in a form emphasizing how primes enter the s...
Abstract. For positive integers n and k, it is possible to choose primes P1, P2, · · · , Pk such ...
Let φ denote the Euler function. For a fixed integer k ≠ 0, we study positive integers n for which t...
Perfect powers in products of terms in an arithmetical progression III by T. N. Shorey (Bombay) and ...
2)2()1() ( =+=+ = xdxdxd infinitely-often. （1） where)(xd represents the number of distinct prime fac...
We study prime divisors of various sequences of positive integers A(n) + 1, n = 1,...,N, such that t...
In this paper, I explore the following problem: Problem. Find instances where a product of distin...
Copyright c © 2013 Rafael Jakimczuk. This is an open access article distributed under the Creative C...