Translations and extensions of the Nicomachus identity

2023/06/30 by Seon-Hong Kim, Kenneth B. Stolarsky, Kim, Seon-Hong +1 · 1 citation
Mathematics · #Advanced Differential Equations and Dynamical Systems #Advanced Topics in Algebra #FOS: Mathematics #Mathematics and Applications #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.2306.17402

openalex publication_date 2023/06/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We search for Nicomachean identities by adding translation parameters, variable parameters, sequence products and adjoining further numbers to sequences. The solutions of definite and indefinite quadratic forms arise in this study of cubic equations obtained from translation parameters. Our search leads to many general Nicomachean-type identities. We also study the geometry of adjoining two numbers to sequences satisfying the Nicomachean identity.

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