On the subsequence of primes having prime subscripts.
On the subset sums of exponential type sequences
On the sum of digits of some sequences of integers
Let b ≥ 2 be a fixed positive integer. We show for a wide variety of sequences {a n}n=1∞ that for almost all n the sum of digits of a n in base b is at least c b log n, where c b is a constant depending on b and on the sequence. Our approach covers several integer sequences arising from number theory and combinatorics.
On the sum of divisors of the Mersenne numbers
On the Sum-of-Divisors Function of the Numbers of Fermat and Ferentinou-Nicolacopoulou
On the theory of cubic residues and nonresidues
On the theory of nth power residues and a conjecture of Kronecker
On the third iterates of the φ- and σ-functions
On the tree structure of the power digraphs modulo
For any two positive integers and , let be a digraph whose set of vertices is and such that there is a directed edge from a vertex to a vertex if . Let be the prime factorization of . Let be the set of all primes dividing and let be such that and . A fundamental constituent of , denoted by , is a subdigraph of induced on the set of vertices which are multiples of and are relatively prime to all primes . L. Somer and M. Křížek proved that the trees attached to all cycle...
On the usual product of rational arithmetic functions
On the values of Euler's φ-function
On the -expansion of an algebraic number in an algebraic base .
On theorems of Niven and Dressler
On two notions of complexity of algebraic numbers
On two supercongruences involving Almkvist-Zudilin sequences
We prove two supercongruences involving Almkvist-Zudilin sequences, which were originally conjectured by Z.-H. Sun (2020).
On various mean values of Dirichlet L-functions
We give a method of obtaining explicit formulas for various mean values of Dirichlet L-functions which are expressed in terms of the Riemann zeta-function, the Euler function and Jordan's totient functions. Applying those results to mean values of Dirichlet L-functions, we also give an explicit formula for certain mean values of double Dirichlet L-functions.
On well distribution modulo 1 and systems of numeration
One property of triangular numbers.
Optimality of the Width- Non-adjacent Form: General Characterisation and the Case of Imaginary Quadratic Bases
We consider digit expansions with an endomorphism of an Abelian group. In such a numeral system, the -NAF condition (each block of consecutive digits contains at most one nonzero) is shown to minimise the Hamming weight over all expansions with the same digit set if and only if it fulfills the subadditivity condition (the sum of every two expansions of weight admits an optimal -NAF).This result is then applied to imaginary quadratic bases, which are used for scalar multiplication in elliptic...
Orderings of the rationals and dynamical systems
This paper is devoted to a systematic study of a class of binary trees encoding the structure of rational numbers both from arithmetic and dynamical point of view. The paper is divided into three parts. The first one is mainly expository and consists in a critical review of rather standard topics such as Stern-Brocot and Farey trees and their connections with continued fraction expansion and the question mark function. In the second part we introduce two classes of (invertible and non-invertible)...