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.
From: Dean Wills [view email]
[v1]
Tue, 2 Jun 2026 06:45:48 UTC (20 KB)
[v2]
Thu, 2 Jul 2026 12:59:47 UTC (20 KB)
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