The Octets of Odd Numbers

Abstract

Translate Article

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.