Distinct subset sums and an inequality for convex functions

Author:
Yong-Gao Chen

Journal:
Proc. Amer. Math. Soc. **128** (2000), 2897-2898

MSC (1991):
Primary 11B13, 11B75, 26A51, 26D15

Published electronically:
April 28, 2000

MathSciNet review:
1695163

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Abstract | References | Similar Articles | Additional Information

Abstract: In this note we prove an inequality for convex functions which implies a conjecture of P. Erdos about a finite integer set with distinct subset sums.

**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**2.**P. E. Frenkel,*Integer sets with distinct subset sums*, Proc. Amer. Math. Soc.**126**(1998), no. 11, 3199–3200. MR**1469406**, 10.1090/S0002-9939-98-04576-6**3.**Takeshi Óno,*A note on spherical quadratic maps over 𝑍*, Algebraic number theory (Kyoto Internat. Sympos., Res. Inst. Math. Sci., Univ. Kyoto, Kyoto, 1976) Japan Soc. Promotion Sci., Tokyo, 1977, pp. 157–161. MR**0447113****4.**Canadian Mathematical Bulletin 17(1975), 768, Problem P.220.**5.**R. Housberger,*Mathematical Gems*III, The Dolciani Mathematical Expositions, 1985, 215-223.

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Additional Information

**Yong-Gao Chen**

Affiliation:
Department of Mathematics, Nanjing Normal University, Nanjing 210097, Jiangsu, People’s Republic of China

Email:
ygchen@pine.njnu.edu.cn

DOI:
https://doi.org/10.1090/S0002-9939-00-05481-2

Received by editor(s):
December 1, 1998

Published electronically:
April 28, 2000

Additional Notes:
The author was supported by the National Nature Science Foundation of China and Fok Ying Tung Education Foundation

Communicated by:
David E. Rohrlich

Article copyright:
© Copyright 2000
American Mathematical Society