On the largest prime factor of the $k-$Fibonacci numbers

Jhon J. Bravo, Florian Luca

Let $P(m)$ denote the largest prime factor of an integer $m\ge 2$, and put $P(0)=P(1)=1$. For an integer $k\ge 2$, let $(F_n^{(k)}{)}_{n\ge 2-k}$ be the $k-$generalized Fibonacc…