Structure of Perfect Numbers Article Swipe

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Edranov, Denis ·

YOU? · · 2025 · Open Access · · DOI: https://doi.org/10.5281/zenodo.17850306

This paper proves the nonexistence of odd perfect numbers by revealing the deep structural nature of perfection. We show that perfect numbers are not arithmetic coincidences but arise solely from binary symmetry: two coherent geometric sequences with base 2 that enable finite convergence to unity and restore divisibility through the Mersenne core. Any attempt to construct a perfect number using odd primes or composite factors fails structurally — new divisors disrupt coherence, and the sum of divisors cannot remain aligned with the number’s lattice. Thus, odd perfect numbers are not merely undiscovered; they are fundamentally impossible. All perfect numbers are fully described by the Euclid–Euler formula.

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Perfect number Mathematics Perfect power Divisibility rule Mersenne prime Discrete mathematics Binary number Base (topology) Natural number Combinatorics Arithmetic Sequence (biology) Square number Divisor (algebraic geometry) Existential quantification Construct (python library) Pure mathematics Perfect field

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Type: preprint
Language: en
Landing Page: https://doi.org/10.5281/zenodo.17850306
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DOI: https://doi.org/10.5281/zenodo.17850306

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Title: Structure of Perfect Numbers

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Type: preprint

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Language: en

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Publication year: 2025

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Publication date: 2025-12-07

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Authors: Edranov, Denis

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Landing page: https://doi.org/10.5281/zenodo.17850306

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Concepts: Perfect number, Mathematics, Perfect power, Divisibility rule, Mersenne prime, Discrete mathematics, Binary number, Base (topology), Natural number, Combinatorics, Arithmetic, Sequence (biology), Square number, Divisor (algebraic geometry), Existential quantification, Construct (python library), Pure mathematics, Perfect field

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