On the problem of Pillai with $k$--generalized Fibonacci numbers and powers of $3$

For an integer $k\ge 2$, let $\{F^{(k)}_{n}\}_{n\ge 2-k}$ be the $k$--generalized Fibonacci sequence which starts with $0, \ldots, 0,1$ (a total of $k$ terms) and for which each term afterwards is the sum of the $k$ preceding terms. In this paper, we find all integers $c$ with at least two representations as a difference between a $k$-generalized Fibonacci number and a power of $3$. This paper continues the previous work of the first author for the Fibonacci numbers, and the Tribonacci numbers.

No reviews yet.

No comments yet.