The Greatest Common Divisor of Shifted Fibonacci Numbers and Shifted Lucas Numbers.

Time: 9:30 -- 11:00, November 22, 2023.
Venue: Room 612, A6, Institute of Mathematics, VAST
Abstract: Let $F_n$ and $L_n$ denote the $n$'th Fibonacci number and Lucas number respectively, and let $k$ be a positive integer. We study necessary and sufficient conditions on $s$ and $t$ so that the functions $n\mapsto \gcd(F_n+s, F_{n+k}+t)$ and $n\mapsto \gcd(L_n+s, L_{n+k}+t)$ are unbounded. Some results on Pell, Pell -- Lucas, Balancing or Lucas -- Balancing numbers are also presented.