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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

A new result concerning the structure of odd perfect numbers


Authors: Peter Hagis and Wayne L. McDaniel
Journal: Proc. Amer. Math. Soc. 32 (1972), 13-15
MSC: Primary 10A25
DOI: https://doi.org/10.1090/S0002-9939-1972-0292740-5
MathSciNet review: 0292740
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Abstract: It is proved here that an odd number of the form $ {p^\alpha }{s^6}$, where s is square-free, p is a prime which does not divide s, and p and $ \alpha $ are both congruent to 1 modulo 4, cannot be perfect.


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DOI: https://doi.org/10.1090/S0002-9939-1972-0292740-5
Keywords: Odd perfect numbers, prime decomposition, exponents
Article copyright: © Copyright 1972 American Mathematical Society