Melham's Conjecture on Odd Power Sums of Fibonacci Numbers
Combinatorics
2015-02-12 v1
Abstract
Ozeki and Prodinger showed that the odd power sum of the first several consecutive Fibonacci numbers of even order is equal to a polynomial evaluated at certain Fibonacci number of odd order. We prove that this polynomial and its derivative both vanish at , and will be an integer polynomial after multiplying it by a product of the first consecutive Lucas numbers of odd order. This presents an affirmative answer to a conjecture of Melham.
Keywords
Cite
@article{arxiv.1502.03294,
title = {Melham's Conjecture on Odd Power Sums of Fibonacci Numbers},
author = {Brian Y. Sun and Matthew H. Y. Xie and Arthur L. B. Yang},
journal= {arXiv preprint arXiv:1502.03294},
year = {2015}
}
Comments
15pages