Translations and extensions of the Nicomachus identity
Number Theory
2023-07-03 v1
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.
Keywords
Cite
@article{arxiv.2306.17402,
title = {Translations and extensions of the Nicomachus identity},
author = {Seon-Hong Kim and Kenneth B. Stolarsky},
journal= {arXiv preprint arXiv:2306.17402},
year = {2023}
}