Seminario: "On the number of residues of certain second-order linear recurrences" - Federico Accossato

"On the number of residues of certain second-order linear recurrences"

Federico Accossato
Politecnico di Torino

Venerdì 2 Febbraio 2024 - ore 15:00
Aula Seminari - Dipartimento di Scienze Matematiche
Politecnico di Torino

Abstract: In this talk, I am going to present some recent results obtained in a joint work with C. Sanna. The central problem is the following: given a polynomial f of degree k, one wants to understand whether there exist a recurrence sequence of integers x=(x_n)_n with characteristic polynomial f, and a positive integer M such that x modulo M has a prescribed number of distinct residues. In the firs part of the seminar, essential groundwork will be laid out to establish the context. This will encompass an overview of prior results and will establish connections with other interesting and relatively old issues in Number Theory.  In the second part, I will focus on our result on the case of certain second order linear recurrences and I will sketch a proof of the main theorem. Special emphasis will be placed on outlining the key ideas behind it.