Tau numbers: a partial proof of a conjecture and other results.
Tauberian theorems for sum sets
The Bouniakowsky conjecture and the density of polynomial roots to prime moduli
The Cantor series of polyadic numbers
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 density of the set of sums
The minimal density of a letter in an infinite ternary square-free word is 883/3215.
The minimal density of a letter in an infinite ternary square-free word is .
The number of relatively prime subsets and phi functions for .
The Romanoff theorem revisited
The size of sums of sets
The topological structure of the set of subsums of an infinite series
Théorie additive des nombres. Densité de Schnirelman
Théorie additive et géométrie des nombres
Totally Brown subsets of the Golomb space and the Kirch space
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 the Golomb topology on the set of natural numbers, as well as the Kirch topology on . Then we examine subsets of these spaces which are totally Brown. Among other results, we characterize the arithmetic progressions which are either totally Brown or totally separated in . We also show that and are aposyndetic. Our results...
Twin prime statistics.