A new result concerning the structure of odd perfect numbers

1972/01/01 by Peter Hagis, Wayne L. McDaniel · 2 citations
Mathematics · #Analytic Number Theory Research #History and Theory of Mathematics #Mathematics and Applications

paper · pdf · doi:10.1090/s0002-9939-1972-0292740-5

openalex publication_date 1972/01/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/31

Abstract

It is proved here that an odd number of the form p^α s⁶, where s is square-free, p is a prime which does not divide s, and p and α are both congruent to 1 modulo 4, cannot be perfect.

Citations

• Untersuchungen über ungerade vollkommene Zahlen.
• Verschärfung der notwendigen Bedingungen für die Existenz von ungeraden vollkommenen Zahlen
• The non-existence of odd perfect numbers of a certain form

Cited by

• A new upper bound for odd perfect numbers of a special form
• Perfect number [wikipedia]