Zentralblatt MATH

Publications of (and about) Paul Erdös

Zbl.No:  015.15203
Autor:  Erdös, Paul; Turán, Pál
Title:  On some sequences of integers. (In English)
Source:  J. London Math. Soc. 11, 261-264 (1936).
Review:  Let a1 < a2 < ··· < ar \leq n be a set of positive integers such that ai-aj\ne aj-ak for 1 \leq k < j < i \leq r. For given n let r(n) be the maximum value of r for which such a set exists. The authors prove that (1)  r(2n) \leq n for n \geq 8, (2) limsup r(n)/n \leq 4/9 . They conjecture that r(n) = o(n), and G.Szekeres conjectures that r(1/2 (3k+1)) = 2k.
Reviewer:  Davenport (Cambridge)
Classif.:  * 11B83 Special sequences of integers and polynomials
Index Words:  Algebra, number theory

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