GCD of sums of $k$ consecutive Fibonacci, Lucas, and generalized Fibonacci numbers

Dan Guyer, aBa Mbirika

We explore the sums of $k$ consecutive terms in the generalized Fibonacci sequence ${\left(G_n\right)}_{n\ge 0}$ given by the recurrence $G_n=G_{n-1}+G_{n-2}$ for all $n \geq 2…