On the problem of Pillai with generalized Fibonacci numbers and powers of 2

Co-authors: C. A. Gomez and F. Luca

For any $k\ge 2$ let $(F_n^{(k)})_{n\ge 0}$ be the $k$-generalized Fibonacci sequence which starts with 0,0,...,0,1 (a total of k terms) and each term afterwards is the sum of the $k$ preceding terms. In the talk, we present all integers $c$ having at least two representations as a difference between a $k$–generalized Fibonacci number and a power of $2$. This extends work done by others for $k=2$ and $k=3$.