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The Octets of the Natural Numbers

Emmanuil Manousos

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Abstract

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 natural numbers are implied: the conjugate of an odd number, the L/R symmetry, the transpose of a natural number and the octets of natural numbers. Using these properties we get a factorization algorithm for natural numbers.

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What this paper is about

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 natural numbers are implied: the conjugate of an odd number, the L/R symmetry, the transpose of a natural number and the octets of natural numbers. Using these properties we get a factorization algorithm for natural numbers.

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Available abstract

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 natural numbers are implied: the conjugate of an odd number, the L/R symmetry, the transpose of a natural number and the octets of natural numbers. Using these properties we get a factorization algorithm for natural numbers.

Key concepts: Natural number, Transpose, Mathematics, Natural (archaeology), Number theory, Factorization, Real number, Combinatorics

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