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Mathematics of Computation
Mathematics of Computation
ISSN 1088-6842(online) ISSN 0025-5718(print)

 

On the equation $\sum _{p|N}\frac{1}{p}+\frac{1}{N}=1$,
pseudoperfect numbers,
and perfectly weighted graphs


Authors: William Butske, Lynda M. Jaje and Daniel R. Mayernik
Journal: Math. Comp. 69 (2000), 407-420
MSC (1991): Primary 11D68; Secondary 11Y50, 05C50
Published electronically: August 19, 1999
MathSciNet review: 1648363
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Abstract | References | Similar Articles | Additional Information

Abstract: We present all solutions to the equation $\sum _{p|N}\frac{1}{p}+\frac{1}{N}=1$ with at most eight primes, improve the bound on the nonsolvability of the Erdös-Moser equation $\sum _{j=1}^{m-1}j^n=m^n$, and discuss the computational search techniques used to generate examples of perfectly weighted graphs.


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Additional Information

William Butske
Affiliation: Department of Mathematics, Wayne State University, 1150 FAB, Detroit, Michigan 48202
Address at time of publication: Department of Mathematics, Purdue University, West Lafayette, Indiana 47906
Email: butske@math.purdue.edu

Lynda M. Jaje
Affiliation: Department of Mathematics, Wayne State University, 1150 FAB, Detroit, Michigan 48202
Address at time of publication: EDS Office Centre, Mailstop 2061, 300 E. Big Beaver Road, Troy, Michigan 48083
Email: lynda.jaje@eds.com

Daniel R. Mayernik
Affiliation: Department of Mathematics, Wayne State University, 1150 FAB, Detroit, Michigan 48202
Email: mayernik@math.wayne.edu

DOI: http://dx.doi.org/10.1090/S0025-5718-99-01088-1
PII: S 0025-5718(99)01088-1
Received by editor(s): June 19, 1996
Received by editor(s) in revised form: March 17, 1998
Published electronically: August 19, 1999
Article copyright: © Copyright 1999 American Mathematical Society