The 99th Fibonacci identity.
The (ABC) Conjecture and the radical index of integers
The additive complements of primes and Goldbach's problem
We extend two results of Ruzsa and Vu on the additive complements of primes.
The Akiyama-Tanigawa algorithm for Bernoulli numbers.
The Akiyama-Tanigawa algorithm for Carlitz's -Bernoulli numbers.
The Akiyama-Tanigawa transformation.
The arithmetic of the coefficients of half-integral weight Eisenstein series
The average length of a trajectory in a certain billiard in a flat two-torus.
The Bernoullian of a Matrix. (A Generalization of the Bernoulli Numbers)
Si associano ad una matrice infinita di un certo tipo altre due matrici dello stesso tipo, dette rispettivamente bernoulliana e antibernoulliana di A. Si studiano alcune proprietà di queste matrici. Si ottiene in tal via una generalizzazione dei classici numeri di Bernoulli.
The Bouniakowsky conjecture and the density of polynomial roots to prime moduli
The Büchi sequences and Hilbert's Tenth Problem
In this short survey paper we state the Büchi conjecture and discuss its relations with the Hilbert Tenth Problem. We give some generalizations of the conjecture, and include some numerical examples.
The Cantor series of polyadic numbers
The cardinality of sumsets: different summands
We offer a complete answer to the following question on the growth of sumsets in commutative groups. Let h be a positive integer and be finite sets in a commutative group. We bound from above in terms of |A|, |A + B₁|, ..., and h. Extremal examples, which demonstrate that the bound is asymptotically sharp in all parameters, are furthermore provided.
The class of Erdős-Turán sets
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 Coefficients of Cosh x/cos x.
The Collatz problem and analogues.
The combinatorialization of linear recurrences.
The combinatorics of certain -ary meta-Fibonacci sequences.
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...