Every odd perfect number has a prime factor which exceeds 
Authors:
Peter Hagis Jr. and Graeme L. Cohen
Journal:
Math. Comp. 67 (1998), 1323-1330
MSC (1991):
Primary 11A25, 11Y70
DOI:
https://doi.org/10.1090/S0025-5718-98-00982-X
MathSciNet review:
1484897
Full-text PDF Free Access
Abstract | References | Similar Articles | Additional Information
Abstract: It is proved here that every odd perfect number is divisible by a prime greater than 
.
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- 3. J. T. Condict, On an Odd Perfect Number's Largest Prime Divisor, Senior Thesis (Middlebury College), May 1978.
- 4. Peter Hagis Jr. and Wayne L. McDaniel, On the largest prime divisor of an odd perfect number. II, Math. Comp. 29 (1975), 922–924. MR 371804, https://doi.org/10.1090/S0025-5718-1975-0371804-2
- 5.
P. Hagis, Jr. and G. L. Cohen, Every odd perfect number has a prime factor which exceeds
(with appendix), Research Report No.93-5 (School of Mathematical Sciences, University of Technology, Sydney), July 1993.
- 6. Wayne L. McDaniel, On multiple prime divisors of cyclotomic polynomials, Math. Comput. 28 (1974), 847–850. MR 0387177, https://doi.org/10.1090/S0025-5718-1974-0387177-4
- 7. Peter L. Montgomery, New solutions of 𝑎^{𝑝-1}≡1 (mod 𝑝²), Math. Comp. 61 (1993), no. 203, 361–363. MR 1182246, https://doi.org/10.1090/S0025-5718-1993-1182246-5
- 8. Trygve Nagell, Introduction to number theory, Second edition, Chelsea Publishing Co., New York, 1964. MR 0174513
- 9. I. Niven, Irrational Numbers, Wiley, New York, 1956. MR 18:195c
, Math. Comp. 61 (1993), 361-363. Retrieve articles in Mathematics of Computation with MSC (1991): 11A25, 11Y70
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Additional Information
Peter Hagis Jr.
Affiliation:
Department of Mathematics, Temple University, Philadelphia, Pennsylvania 19122
Graeme L. Cohen
Affiliation:
Department of Mathematics, Temple University, Philadelphia, Pennsylvania 19122;
School of Mathematical Sciences, University of Technology, Sydney, Broadway, NSW 2007, Australia
Email:
g.cohen@maths.uts.edu.au
DOI:
https://doi.org/10.1090/S0025-5718-98-00982-X
Received by editor(s):
October 24, 1995
Received by editor(s) in revised form:
July 10, 1996
Article copyright:
© Copyright 1998
American Mathematical Society
