Number Theory

    

Sums of Powers of Fibonacci and Lucas Numbers and their Related Integer Sequences

Authors: Ryan Zielinski

In this paper we will look at sums of odd powers of Fibonacci and Lucas numbers of even indices. Our motivation will be conjectures, now theorems, which go back to Melham. Using the simple approach of telescoping sums we will be able to give new proofs of those results. Along the way we will establish inverse relationships for such sums and discover new integer sequences.

Comments: 28 Pages. This work is licensed under the CC BY 4.0, a Creative Commons Attribution License.

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[v1] 2020-06-19 15:30:28

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