Double Counting and Fibonacci Numbers

Dr. Ivaylo Kortezov, Assoc. Prof.
Institute of Mathematics and Informatics
Bulgarian Academy of Sciences

https://doi.org/10.53656/math2024-3-7-dou

Absract. The article proposes a double counting method for proving combinatorial identities involving Fibonacci numbers. The method is easily remembered by the students. It allows them to apply it creatively in many situations, by (re)discovering the results by themselves and asking meaningful questions. The method is mainly oriented towards preparation for mathematical competitions.
Keywords: combinatorial identities; double counting; Fibonacci sequence; math contests

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