Type: Article

Coincidences in generalized Fibonacci sequences

Bravo, Jhon J.; Luca, Florian;

Abstract:

The k-generalized Fibonacci sequence (F-n((k)))(n) resembles the Fibonacci sequence in that it starts with 0, ... ,0, 1 (k terms) and each term afterwards is the sum of the k preceding terms. In this paper, we are interested in finding the integers that appear in different generalized Fibonacci sequences; i.e., we study the Diophantine equation F-n((k)) = F-m((l)) in positive integers n, k, m, l with k, l >= 2.