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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
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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Keywords: Odd perfect numbers, prime decomposition, exponents
Article copyright: © Copyright 1972 American Mathematical Society

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