New York Journal of Mathematics
Volume 16 (2010) 23-30


Florian Luca and Carl Pomerance

On the radical of a perfect number

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Published: April 28, 2010
Keywords: perfect number, ABC conjecture
Subject: 11A25

In this note, we look at the radical (that is, the squarefree kernel) of perfect numbers. We raise the question of whether large perfect numbers have the tendency to become far apart from each other and prove several results towards this under the ABC conjecture.


F. L. was supported in part by grants SEP-CONACyT 79685 and PAPIIT 100508
C. P. was supported in part by NSF grant DMS-0703850

Author information

Florian Luca:
Instituto de Matemáticas, Universidad Nacional Autonoma de México, C.P. 58089, Morelia, Michoacán, México

Carl Pomerance:
Mathematics Department, Dartmouth College, Hanover, NH 03755, USA