Some Recent Developments in three Classical Problems of Number Theory.
Sommes des chiffres et nombres presque premiers.
Sul carattere di una particolare congruenza.
Sum of higher divisor function with prime summands
Let be an integer. Recently, Hu and Lü offered the asymptotic formula for the sum of the higher divisor function where represents the th divisor function. We give the Goldbach-type analogy of their result. That is to say, we investigate the asymptotic behavior of the sum where are prime variables.
Sumsets without powerful numbers
Sur certaines hypothèses concernant les nombres premiers
Sur la fréquence des nombres premiers
Sur la limite du degré des groupes primitifs qui contiennent une substitution donnée.
Sur la représentation graphique des diviseurs des nombres
Sur les facteurs premiers distincts d'entiers consécutifs
Sur quelques théorèmes d'arithmétique
Test de primalité et méthodes de factorisation
Tests de primalité d'après Adleman, Rumely, Pomerance et Lenstra
The closures of arithmetic progressions in the common division topology on the set of positive integers
In this paper we characterize the closures of arithmetic progressions in the topology T on the set of positive integers with the base consisting of arithmetic progressions {an + b} such that if the prime number p is a factor of a, then it is also a factor of b. The topology T is called the common division topology.
The common division topology on
A topological space is totally Brown if for each and every nonempty open subsets of we have . Totally Brown spaces are connected. In this paper we consider a topology on the set of natural numbers. We then present properties of the topological space , some of them involve the closure of a set with respect to this topology, while others describe subsets which are either totally Brown or totally separated. Our theorems generalize results proved by P. Szczuka in 2013, 2014, 2016 and by...
The factorial representations of integers and the Eratosthenes sieve
The generalization and proof of Bertrand's postulate.
The greatest prime factor of
The Gross-Koblitz formula revisited
The mantissa distribution of the primorial numbers
We show that the sequence of mantissas of the primorial numbers Pₙ, defined as the product of the first n prime numbers, is distributed following Benford's law. This is done by proving that the values of the first Chebyshev function at prime numbers are uniformly distributed modulo 1. We provide a convergence rate estimate. We also briefly treat some other sequences defined in the same way as Pₙ.