【摘 要】
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Let Fn denote the nth Fibonacci number and Ln denote the nth Lucas number.Melham conjectured that for any n, m ≥ 1, the sum L1L3L5 … L2m+1 Σr=1 F2m2r+1can be
【机 构】
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CenterforCombinatorics,NankaiUniversity
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Let Fn denote the nth Fibonacci number and Ln denote the nth Lucas number.Melham conjectured that for any n, m ≥ 1, the sum L1L3L5 … L2m+1 Σr=1 F2m2r+1can be expressed as (F2n+1-1)2P2m-1(F2n+1), where P2m-1(x) is a polynomial of degree 2m-1 with integer coefficients.Based on a formula due to Prodinger, we give an affirmative answer to Melhams conjecture.This is a joint work with Brian Y.Sun and Matthew H.Y.Xie.
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