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Integer sets with distinct subset sums
Author(s):
P.
E.
Frenkel
Journal:
Proc. Amer. Math. Soc.
126
(1998),
3199-3200.
MSC (1991):
Primary 11B13;
Secondary 11B75
MathSciNet review:
1469406
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Abstract:
We give a simple, elementary new proof of a generalization of the following conjecture of Paul Erdos: the sum of the elements of a finite integer set with distinct subset sums is less than 2.
References:
- 1.
- S. J. Benkoski and P. Erd\H{o}s, On weird and pseudoperfect numbers, Math. Comp. 28 (1974), 617-623. MR 50:228; MR 50:12902
- 2.
- F. Hanson, J. M. Steele and F. Stenger, Distinct sums over subsets, Proc. Amer. Math. Soc. 66 (1977), 179-180. MR 56:5482
- 3.
- Canadian Mathematical Bulletin 17 (1975), 768, Problem P. 220.
- 4.
- R. Housberger, Mathematical Gems III, The Dolciani Mathematical Expositions, 1985, 215-223.
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Additional Information:
P.
E.
Frenkel
Affiliation:
Kútvölgyi út 40, Budapest 1125, Hungary
Email:
frenkelp@cs.elte.hu
DOI:
10.1090/S0002-9939-98-04576-6
PII:
S 0002-9939(98)04576-6
Keywords:
Sequences,
subset sums
Received by editor(s):
April 7, 1997
Additional Notes:
The author thanks L. Laczkó for calling his attention to the problem, and M. Laczkovich for his attention and kind help.
Communicated by:
David E. Rohrlich
Copyright of article:
Copyright
1998,
American Mathematical Society
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