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The Octets of Odd Numbers

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  • Emmanuil Manousos

    (APM Institute for the Advancement of Physics and Mathematics, Greece)

Abstract

In this paper we present a coherent network of concepts, theorems, propositions, and corollaries that arise from a theorem. A linear combination of powers of two uniquely represents every odd number except 1. The powers of 2 are consecutive with the coefficients −1 or +1. From this representation, a set of mathematical concepts leads to a mathematical object, the octets of odd numbers. We studied the properties of octets and their relationship to the structure of odd numbers. Thus, a new framework for the study of natural numbers emerges.

Suggested Citation

Handle: RePEc:epw:ejmath:v:6:y:2025:i:5:id:14412
DOI: 10.24018/ejmath.2025.6.5.412
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