On sum-free subsequences

Author:
David G. Cantor

Journal:
Proc. Amer. Math. Soc. **43** (1974), 67-68

MSC:
Primary 10L10

DOI:
https://doi.org/10.1090/S0002-9939-1974-0374078-2

MathSciNet review:
0374078

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Abstract: A sequence of real numbers is said to be *sum-free* if no number of the sequence is the sum of distinct elements of the same sequence. In this paper we show that a sequence of positive real numbers has a sum-free subsequence containing at least elements.

**[1]**S. L. G. Choi,*The largest sum-free subsequence from a sequence of 𝑛 numbers*, Proc. Amer. Math. Soc.**39**(1973), 42–44. MR**0313216**, https://doi.org/10.1090/S0002-9939-1973-0313216-3**[2]**P. Erdős,*Extremal problems in number theory*, Proc. Sympos. Pure Math., Vol. VIII, Amer. Math. Soc., Providence, R.I., 1965, pp. 181–189. MR**0174539**

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DOI:
https://doi.org/10.1090/S0002-9939-1974-0374078-2

Article copyright:
© Copyright 1974
American Mathematical Society