一个Merca恒等式的组合证明

Combinatorial Proof of an Identity of Merca

摘要: 本文基于Merca研究中提出的一个恒等式，Merca通过代数方法对其进行了证明，而我们从组合数学的角度入手，给出了该恒等式的一个全新的组合证明。相比代数证明，我们发现组合证明过程更加直观和简洁，提供了对该恒等式更深层次的结构性理解。

Abstract: This paper is based on an identity proposed by Merca, which was originally proved by using algebraic method. From the perspective of combinatorics, we present a new combinatorial proof of this identity. Compared to the algebraic approach, our combinatorial proof is more intuitive and concise, which offers a deeper structural understanding of the identity.