La 5ième petite journée GANDA

IMB le 26 novembre 2021

Résumés des exposés

Florian LUCA (Johannesburg et Bordeaux)
Carmichael numbers of the form 2^n k + 1
In the first part of the talk we will survey some results concerning Carmichael numbers of the form \(2^n k+1\). Then we will present the proof of the fact that there is no Carmichael number of the above form with \(k\) prime.

Haojie HONG (Bordeaux)
Stewart's theorem on prime factors of linear recurrences and its explicit version

In 2013, C. L. Stewart proved that the largest prime divisor of the \(n\)th term of a Lucas sequence of integers grows quicker than \(n\) if \(n\) is greater than some constant \(C\), answering questions posed by Erdős and Schinzel. However, Stewart did not give an explicit expression of \(C\). In this talk, I will introduce his theorem and speak on our work on an explicit version.

Bernadette FAYE (Saint-Louis)
Repdigits in various linear recurrent sequences

Given an integer \(g>1\), a base \(g\)-repdigit is a number of the form \[ N=a\cdot\frac{g^m-1}{g-1} \] for some \(m\geq 1\) and \(a\in\{1,\ldots,(g-1)\}\). When \(g=10\), such number are better know as a repdigit. Recently, investigation of the repdigits in the second-order linear recurrence sequences has been of interest to mathematicians. In this talk, we will make a survey of the recents results obtained on this subject.

Jean-Marc DESHOUILLERS (Bordeaux)
Randomness and non-randomness in Piatetski-Shapiro sequences

Résumé

Avec de soutien de l'IMB, de l'IRN CNRS « GANDA » et du projet ANR JINVARIANT

           

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