Number Theory

    

The Structural Parity Paradox - Perfect Numbers

Authors: James DeCoste

This paper presents a clean, structural reframing of the Perfect Number Conjecture by analyzing the even/odd parity balance of proper divisors. By reverse-engineering the factor architecture from the inside out, we show that even perfect numbers are governed by a rigid, doubling arithmetic engine that isolates exactly one odd divisor. We prove that this specific geometric distribution forces a structural "snapping lock" with the number 1, creating an airtight parity barrier that physically outlaws odd perfect numbers from existing in the natural number line.

Comments: 4 Pages.

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[v1] 2026-10-27 00:32:52

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