More Combinatorial Proofs via Flagpole Arrangements

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In their recent book [1], Arthur Benjamin and Jennifer Quinn derive a wide array of algebraic and number theoretic identities with clever applications of elementary counting principles. As they say, While [counting is] not necessarily the simplest approach, it offers another method to gain understanding of mathematical truths. To a combinatorialist, this kind of proof is the only right one. A sampling of the combinatorial approach was presented in [2], which also issued a challenge to the reader to find a combinatorial proof of the identity