Integer sets with distinct subset sums

Author:
P. E. Frenkel

Journal:
Proc. Amer. Math. Soc. **126** (1998), 3199-3200

MSC (1991):
Primary 11B13; Secondary 11B75

DOI:
https://doi.org/10.1090/S0002-9939-98-04576-6

MathSciNet review:
1469406

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Abstract | References | Similar Articles | Additional Information

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.

**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:
https://doi.org/10.1090/S0002-9939-98-04576-6

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

Article copyright:
© Copyright 1998
American Mathematical Society