Number Theory

    

The Octets of the Natural Numbers

Authors: Emmanuil Manousos

"Every natural number, with the exception of 0 and 1, can be written in a unique way as a linear combination of consecutive powers of 2, with the coefficients of the linear combination being -1 or +1" From this Theorem, four fundamental properties of odd numbers are implied: the conjugate of an odd number, the L/R symmetry, the transpose of an odd number and the octets of odd numbers. These concepts are used to obtain a classification of odd numbers and an algorithm for finding the factors of composite Fermat numbers.

Comments: 23 Pages.

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Submission history

[v1] 2021-03-25 13:21:24
[v2] 2022-07-18 18:38:54
[v3] 2023-10-09 17:25:11
[v4] 2023-12-20 19:42:51

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