On sequences not containing a large sum-free subsequence

Author:
S. L. G. Choi

Journal:
Proc. Amer. Math. Soc. **41** (1973), 415-418

MSC:
Primary 10L05

DOI:
https://doi.org/10.1090/S0002-9939-1973-0325563-X

MathSciNet review:
0325563

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Abstract: A subsequence of a sequence of integers is said to be sum-free if no integer of the subsequence is the sum of distinct integers of this same subsequence. In this paper we shall prove, provided is sufficiently large, that there exists a sequence of integers whose largest sum-free subsequence has at most integers, where is an absolute constant.

**[1]**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****[2]**P. Varnavides,*On certain sets of positive density*, J. London Math. Soc.**34**(1959), 358–360. MR**0106865**, https://doi.org/10.1112/jlms/s1-34.3.358

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Additional Information

DOI:
https://doi.org/10.1090/S0002-9939-1973-0325563-X

Keywords:
Sum-free,
subsequence,
arithmetic progressions

Article copyright:
© Copyright 1973
American Mathematical Society