On some combinations of k-nacci numbers.

For k ≥ 2, the k -generalized Fibonacci sequence ( F n ( k ) ) n is defined by the initial values 0 , 0 , … , 0 , 1 ( k terms) and such that each term afterwards is the sum of the k preceding terms. In this paper, we shall study for which x, k and t the expression x t F n + t ( k ) + ⋯ + x F n + 1 ( k ) + F n ( k ) belongs to ( F m ( k ) ) m for infinitely many integers n . This work generalizes [13, Theorem 2] which is related to the case t = 1 . [ABSTRACT FROM AUTHOR]