2015/02/11 by Brian Y. Sun, Sun, Brian Y., Matthew H. Y. Xie +3
Mathematics · Physics and Astronomy · #05A19 #11B39 #Advanced Combinatorial Mathematics #Advanced Mathematical Identities #Advanced Mathematical Theories and Applications #Combinatorics (math.CO) #FOS: Mathematics #math.CO #msc:05A19 #msc:11B39
paper · pdf · doi:10.48550/arxiv.1502.03294
15pages
arxiv created 2015/02/11 · openalex publication_date 2015/02/11 · arxiv updated 2015/02/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.