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arXiv · 2606.03228

Cassini's identity for k-bonacci numbers

Harold R. Parks·Dean C. Wills
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Abstract

Efforts have been made to extend Cassini's identity (also known as Simson's identity) to the k-step or k-bonacci numbers for decades. These efforts have lacked both completeness of result and simplicity of proof, and this question remains open and relevant. In this note, we offer a definitive solution as well as the generalization of both Catalan's and Vajda's identities.

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Harold R. Parks, Dean C. Wills. 2026-07-02. Cassini's identity for k-bonacci numbers. https://arxiv.org/abs/2606.03228

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