The moments of split greatest common divisors

Abhishek Jha, Ayan Nath, Emanuele Tron

Sequences of the form $(\gcd (u_n,v_n){)}_{n\in \mathbb{N}}$, with $(u_n{)}_n$, $(v_n{)}_n$ sums of $S$-units, have been considered by several authors. The study of $\gcd (n,u_n)$ correspo…