New results about certain sums S n (k) of products of the Lucas numbers are derived. These sums are related to the generating function of the k-th powers of the Fibonacci numbers. The sums for S n (k) are expressed by the binomial and the Fibonomial coefficients. Proofs of these formulas are based on a special inverse formula.
The aim of this paper is to give new results about factorizations of the Fibonacci numbers F n and the Lucas numbers L n. These numbers are defined by the second order recurrence relation a n+2 = a n+1 + a n with the initial terms F 0 = 0, F 1 = 1 and L 0 = 2, L 1 = 1, respectively. Proofs of theorems are done with the help of connections between… (More)