Coincidences in generalized Fibonacci sequences

Abstract: The k-generalized Fibonacci sequence resembles the Fibonacci sequence in that it starts with (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 in positive integers n, k, m, ℓ with . [Copyright &y& Elsevier]