Mathematics of Computation

Published by the American Mathematical Society since 1960 (published as Mathematical Tables and other Aids to Computation 1943-1959), Mathematics of Computation is devoted to research articles of the highest quality in computational mathematics.

ISSN 1088-6842 (online) ISSN 0025-5718 (print)

The 2024 MCQ for Mathematics of Computation is 1.78.

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Odd perfect numbers, Diophantine equations, and upper bounds
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by Pace P. Nielsen;
Math. Comp. 84 (2015), 2549-2567
DOI: https://doi.org/10.1090/S0025-5718-2015-02941-X
Published electronically: February 18, 2015

Abstract:

We obtain a new upper bound for odd multiperfect numbers. If $N$ is an odd perfect number with $k$ distinct prime divisors and $P$ is its largest prime divisor, we find as a corollary that $10^{12}P^{2}N<2^{4^{k}}$. Using this new bound, and extensive computations, we derive the inequality $k\geq 10$.
References
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Bibliographic Information
  • Pace P. Nielsen
  • Affiliation: Department of Mathematics, Brigham Young University, Provo, Utah 84602
  • MR Author ID: 709329
  • Email: pace@math.byu.edu
  • Received by editor(s): June 14, 2013
  • Received by editor(s) in revised form: December 16, 2013
  • Published electronically: February 18, 2015
  • © Copyright 2015 American Mathematical Society
  • Journal: Math. Comp. 84 (2015), 2549-2567
  • MSC (2010): Primary 11N25; Secondary 11Y50
  • DOI: https://doi.org/10.1090/S0025-5718-2015-02941-X
  • MathSciNet review: 3356038