Odd perfect numbers, Diophantine equations, and upper bounds
Author:
Pace P. Nielsen
Journal:
Math. Comp. 84 (2015), 2549-2567
MSC (2010):
Primary 11N25; Secondary 11Y50
DOI:
https://doi.org/10.1090/S0025-5718-2015-02941-X
Published electronically:
February 18, 2015
MathSciNet review:
3356038
Full-text PDF Free Access
Abstract | References | Similar Articles | Additional Information
Abstract: We obtain a new upper bound for odd multiperfect numbers. If is an odd perfect number with
distinct prime divisors and
is its largest prime divisor, we find as a corollary that
. Using this new bound, and extensive computations, we derive the inequality
.
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Additional Information
Pace P. Nielsen
Affiliation:
Department of Mathematics, Brigham Young University, Provo, Utah 84602
MR Author ID:
709329
Email:
pace@math.byu.edu
DOI:
https://doi.org/10.1090/S0025-5718-2015-02941-X
Keywords:
Diophantine equation,
perfect number
Received by editor(s):
June 14, 2013
Received by editor(s) in revised form:
December 16, 2013
Published electronically:
February 18, 2015
Article copyright:
© Copyright 2015
American Mathematical Society