Quelques mots sur la droite projective réelle
Rational base number systems for p-adic numbers
This paper deals with rational base number systems for p-adic numbers. We mainly focus on the system proposed by Akiyama et al. in 2008, but we also show that this system is in some sense isomorphic to some other rational base number systems by means of finite transducers. We identify the numbers with finite and eventually periodic representations and we also determine the number of representations of a given p-adic number.
Rational base number systems for p-adic numbers
This paper deals with rational base number systems for p-adic numbers. We mainly focus on the system proposed by Akiyama et al. in 2008, but we also show that this system is in some sense isomorphic to some other rational base number systems by means of finite transducers. We identify the numbers with finite and eventually periodic representations and we also determine the number of representations of a given p-adic number.
Représentation multiplicative des entiers et fonctions multiplicatives
Some Remarkable Identities Involving Numbers
The article focuses on simple identities found for binomials, their divisibility, and basic inequalities. A general formula allowing factorization of the sum of like powers is introduced and used to prove elementary theorems for natural numbers. Formulas for short multiplication are sometimes referred in English or French as remarkable identities. The same formulas could be found in works concerning polynomial factorization, where there exists no single term for various identities. Their usability...
Sur les Systèmes Numériqes de Cantor
Sur un procédé universel d'extraction
On étudie ici un procédé universel d’extraction de suites - extraction en un sens élargi qui sera précisé - consistant à piquer les chiffres de l’écriture en base des indices de la suite, cela suivant une partie de . On s’intéresse plus particulièrement à l’action de ce procédé sur les suites périodiques, en liaison avec la régularité de la partie , en termes de périodicité, de quasi-périodicité et d’automaticité. Ainsi (à une restriction évidente près), les procédés associés aux parties ultimement...
The representation of real numbers by infinite series of rationals
The Zeckendorf expansion of polynomial sequences
In the first part of the paper we prove that the Zeckendorf sum-of-digits function and similarly defined functions evaluated on polynomial sequences of positive integers or primes satisfy a central limit theorem. We also prove that the Zeckendorf expansion and the -ary expansions of integers are asymptotically independent.