Seminario: "Some results on the greatest common divisors of terms of linear recurrences" - Carlo Sanna

Online seminar for the Faculty of Mathematics and Computer Science of the Jagiellonian University (Kraków).

"Some results on the greatest common divisors of terms of linear recurrences"

Carlo Sanna  - Politecnico di Torino

Giovedì 5 gennaio 2023 - ore 14:30
Faculty of Mathematics and Computer Science of the Jagiellonian University, online

Abstract: Let (F_n) be the sequence of Fibonacci numbers, which is defined as usual by F1 = F2 = 1 and F_{n+2} = F_{n+1} + F_n. In this talk we will: survey several results on the greatest common divisors of n and F_n; show the techniques behind their proofs; and pose some related open problems. Generalization to Lucas sequence will be also considered. Part of the interest in studying gcd(n, F_n) resides in the fact that this task can be considered a simpler, albeit nontrivial, case of the general problem of studying the greatest common divisor of terms of two linear recurrences; a problem that led to the famous Bugeaud–Corvaja–Zannier bound and the difficult open conjecture of Ailon and Rudnick.

Slides dell'evento: Le slide del seminario posso essere scaricate qui (1,09 MB).

Video dell'evento: La registrazione del seminario è disponibile sul Canale YouTube del gruppo CrypTO.
Video