Melham's Conjecture on Odd Power Sums of Fibonacci Numbers |
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Authors: | Brian Y Sun Matthew HY Xie |
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Institution: | Center for Combinatorics, LPMC, Nankai University, Tianjin 300071, P.R. China. |
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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 a 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 a?rmative answer to a conjecture of Melham. |
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Keywords: | 11B39 05A19 |
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