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Melham's Conjecture on Odd Power Sums of Fibonacci Numbers
- Publication Year :
- 2015
-
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 $1$, 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.<br />Comment: 15pages
- Subjects :
- Mathematics - Combinatorics
11B39, 05A19
Subjects
Details
- Database :
- arXiv
- Publication Type :
- Report
- Accession number :
- edsarx.1502.03294
- Document Type :
- Working Paper