Subsequences and Divisibility by Powers of the Fibonacci Numbers

Kritkajohn Onphaeng, Prapanpong Pongsriiam

Let $F_n$ be the $n$th Fibonacci number. Let $m,n$ be positive integers. Define a sequence $(G(k,n,m){)}_{k\ge 1}$ by $G(1,n,m)=F_n^m$, and $G(k+1,n,m)=F_{nG(k,n,m)}$ for all $…