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On a problem of P. Erdős

  • E. Szemerédi (a1)


The letters a, b, n, m, t (perhaps with suffixes) always denote natural numbers. A, B, S denote finite sets of natural numbers. |A| stands for the cardinality of A.

For a given constant c > 1 we say that the set A has property α(c) if there are at most c|A| differences ab ≥ 0 for a, bA.



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1. Roth, K. F., “On certain sets of integers”, J. London Math. Soc., 28 (1953), 104109.
2. Szemerédi, E., “On sets of integers containing no four elements in arithmetic progression”, Acta Math. Acad. Sci. Hung., 20 (1969), 89104.
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