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

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. Erdős,*On weird and pseudoperfect numbers*, Math. Comp.**28**(1974), 617–623. MR**0347726**, 10.1090/S0025-5718-1974-0347726-9

Sidney Kravitz,*Corrigendum: “On weird and pseudoperfect numbers” (Math. Comp. 28 (1974), 617–623) by S. J. Benkoski and P. Erdős*, Math. Comp.**29**(1975), 673. MR**0360452**, 10.1090/S0025-5718-1975-0360452-6**2.**F. Hanson, J. M. Steele, and F. Stenger,*Distinct sums over subsets*, Proc. Amer. Math. Soc.**66**(1977), no. 1, 179–180. MR**0447167**, 10.1090/S0002-9939-1977-0447167-4**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