A Fibonacci-Counting Proof Begged by Benjamin and Quinn

By Doron Zeilberger

[Also presented at the 11th Fibonacci Conference, and published in its proceedings in Congressus Numerantium 194 (Jan. 2009), 263-264.]

Written: May 24 2004

When I was young and handsome, I couldn't see an identity without trying to prove it bijectively. Somehow, I weaned myself of this addiction. But the urge got rekindled, when I read Arthur Benjamin and Jennifer Quinn's masterpiece `Proofs that Really Count', that contained some challenges that the authors couldn't do (or so they said). This is the result. It was derived using a meta-algorithm that converts `ugly manipulatorics proofs' into `beautiful bijective proofs', that I hope to describe elsewhere (and program, so that Shalosh can start doing these bijective proofs).

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