Terms of Generalized Fibonacci Sequences That are Powers of Their Orders.

For k ≥ 2, the k-generalized Fibonacci sequence ( F ) is defined by the initial values 0 ,0 ,..., 0 , 1 ( k terms) so that each term afterward is the sum of the k preceding terms. In this paper, we prove that the only solution of the Diophantine equation F = k = k with t > 1 and m > k+ 1 ≥ 4 is F = 3. [ABSTRACT FROM AUTHOR]