NYJM Abstract - 16-3 - Florian Luca and Carl Pomerance

Florian Luca and Carl Pomerance

On the radical of a perfect number

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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

Florian Luca:
Instituto de Matemáticas, Universidad Nacional Autonoma de México, C.P. 58089, Morelia, Michoacán, México
fluca@matmor.unam.mx

Carl Pomerance:
Mathematics Department, Dartmouth College, Hanover, NH 03755, USA
carl.pomerance@dartmouth.edu