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{\bf Arthur T. Benjamin, Alex K. Eustis, and Sean S. Plott}
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{\bf The 99th Fibonacci Identity}
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We provide elementary combinatorial proofs of several Fibonacci and
Lucas number identities left open in the book {\it Proofs That
Really Count} [1], and generalize these to Gibonacci sequences $G_n$
that satisfy the Fibonacci recurrence, but with arbitrary real
initial conditions. We offer several new identities as well. Among
these, we prove $\sum_{k\geq 0}{n \choose k}G_{2k} = 5^n G_{2n}$ and
$\sum_{k\geq 0}{n \choose k}G_{qk}(F_{q-2})^{n-k} = (F_q)^n G_{2n}$.

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