A Fundamental Contradiction Proving the Non-Existence of Odd Perfect Numbers
Year: 2025
Type: article
Abstract: A perfect number is a positive integer N that equals the sum of its properdivisors. While even perfect numbers have been classified, the existence of an oddperfect number remains an open question in number theory. In this paper, wepresent a contradiction that arises in the divisor structure of any hypothetical oddperfect number. Specifically, we demonstrate that the largest proper divisor mustbe N/2, which cannot be an integer for an odd N. This contradiction invalidatesthe necessary conditions for a perfect number, thereby proving that no odd perfect number can exist.
Author: Madhukar Jagannath Jadhav
Language: English
Subfield: Algebra and Number Theory
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W6930738477
FWCI:
Cites:
Cited by:
Related to: