Sequential convergences on generalized Boolean algebras
In this paper we investigate convergence structures on a generalized Boolean algebra and their relations to convergence structures on abelian lattice ordered groups.
Serie de Lucas y criptografía.
Séries formelles et produit de Hadamard
Nous nous intéressons ici essentiellement à l’algèbre de Hadamard des séries formelles. Si des résultats importants ont été obtenus dans le cas d’une variable, il n’en est pas de même dans le cas de plusieurs variables. En effet, beaucoup de problèmes posés restent encore sans réponse. C’est le cas par exemple du problème du quotient de Hadamard, ou celui de la caractérisation des éléments de Hadamard inversibles, ou les diviseurs de zéro, ou encore le problème des multiplicateurs de certains sous-ensembles...
Set-polynomials and polynomial extension of the Hales-Jewett theorem.
Sets, lists and noncrossing partitions.
Sets of integers and quasi-integers with pairwise common divisor
Sets of integers that do not contain long arithmetic progressions.
Sets of integers with pairwise common divisor and a factor from a specified set of primes
Sets of -recurrence but not -recurrence
For every , we produce a set of integers which is -recurrent but not -recurrent. This extends a result of Furstenberg who produced a -recurrent set which is not -recurrent. We discuss a similar result for convergence of multiple ergodic averages. We also point out a combinatorial consequence related to Szemerédi’s theorem.
Sets of lengths do not characterize numerical monoids.
Sets of positive integers with prescribed values of densities
Sets of Primes with Intermediate Density.
Sets with even partition functions and 2-adic integers. II.
Sets with more sums than differences.
Sets with prescribed lower and upper weighted densities.
Several generating functions for second-order recurrence sequences.
Short character sums with Fermat quotients
Short remark on Fibonacci-Wieferich primes
This paper has been inspired by the endeavour of a large number of mathematicians to discover a Fibonacci-Wieferich prime. An exhaustive computer search has not been successful up to the present even though there exists a conjecture that there are infinitely many such primes. This conjecture is based on the assumption that the probability that a prime is Fibonacci-Wieferich is equal to . According to our computational results and some theoretical consideratons, another form of probability can...
Sidon basis in polynomial rings over finite fields
Let denote the polynomial ring over , the finite field of elements. Suppose the characteristic of is not or . We prove that there exist infinitely many such that the set contains a Sidon set which is an additive basis of order .
Sign changes of certain arithmetical function at prime powers
We examine an arithmetical function defined by recursion relations on the sequence and obtain sufficient condition(s) for the sequence to change sign infinitely often. As an application we give criteria for infinitely many sign changes of Chebyshev polynomials and that of sequence formed by the Fourier coefficients of a cusp form.