On sequences not containing a large sumfree subsequence
Author:
S. L. G. Choi
Journal:
Proc. Amer. Math. Soc. 41 (1973), 415418
MSC:
Primary 10L05
MathSciNet review:
0325563
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Abstract: A subsequence of a sequence of integers is said to be sumfree 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 sumfree 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
(30 #4740)
 [2]
P.
Varnavides, On certain sets of positive density, J. London
Math. Soc. 34 (1959), 358–360. MR 0106865
(21 #5595)
 [1]
 P. Erdös, Extremal problems in number theory, Proc. Sympos. Pure Math., vol. 8, Amer. Math. Soc., Providence, R.I., 1965, pp. 181189. MR 30 #4740. MR 0174539 (30:4740)
 [2]
 P. Varnavides, On certain sets of positive density, J. London Math. Soc. 34 (1959), 358360. MR 21 #5595. MR 0106865 (21:5595)
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Additional Information
DOI:
http://dx.doi.org/10.1090/S0002993919730325563X
PII:
S 00029939(1973)0325563X
Keywords:
Sumfree,
subsequence,
arithmetic progressions
Article copyright:
© Copyright 1973
American Mathematical Society
