Proof of the odd perfect number conjecture

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Authors: Y Liu
Cited by: 0

Abstract

The odd-perfect divisor conjecture is a classic problem in the field of number theory. The core question is whether there is a positive odd number that satisfies “the sum of all true divisors is equal to itself”. This article will be based on the premise assumption that “there are positive infinite odd numbers” and follow the established logical deduction to prove that odd perfect numbers do not exist, that is, the conjecture of odd perfect numbers does not hold.

Fields of Study & Subjects

Analytic Number Theory Research Advanced Mathematical Theories Algebraic Geometry and Number Theory

Publication details

Publication date
14 January 2026
Document type
Preprint