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

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Abstract | References | Similar Articles | Additional Information

Abstract: It is proved here that every odd perfect number is divisible by a prime greater than .

**1.**A. S. Bang,*Taltheoretiske Undersøgelser*, Tidsskrift Math.**5, IV**(1886), 70-80, 130-137.**2.**M. S. Brandstein,*New lower bound for a factor of an odd perfect number*, Abstracts of the Amer. Math. Soc.**3**(1982), 257.**3.**J. T. Condict,*On an Odd Perfect Number's Largest Prime Divisor*, Senior Thesis (Middlebury College), May 1978.**4.**P. Hagis, Jr. and W. L. McDaniel,*On the largest prime divisor of an odd perfect number. II*, Math. Comp.**29**(1975), 922-924. MR**51:8021****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.**W. L. McDaniel,*On multiple prime divisors of cyclotomic polynomials*, Math. Comp.**28**(1974), 847-850. MR**52:8022****7.**P. L. Montgomery,*New solutions of*, Math. Comp.**61**(1993), 361-363. MR**94d:11003****8.**T. Nagell,*Introduction to Number Theory, second edition*, Chelsea, New York, 1964. MR**30:4714****9.**I. Niven,*Irrational Numbers*, Wiley, New York, 1956. MR**18:195c**

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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