## Zentralblatt MATH

Publications of (and about) Paul Erdös

Zbl.No:  209.35402
Autor:  Erdös, Paul; Rényi, Alfréd
Title:  On some applications of probability methods to additive number theoretic problems (In English)
Source:  Contrib. Ergodic Theory Probab., Lecture Notes Math. 160, 37-44 (1970).
Review:  [For the entire collection see Zbl 202.05002.]
The authors prove that to every \alpha, 0 < \alpha < 1 there is a sequence A of density \alpha so that for very sequence of integers b1 < ... < bk the density of \bigcupki = 1 {A+bi} is 1-(1-\alpha)k. The theorem no longer holds if 1-(1-\alpha)k is replaced by 1-(1-\alpha)k+\epsilon. But the authors believe that there is a sequence of density \alpha so that the density of \bigcupki = 1 {A+bi} is always greater than 1-(1-\alpha)k. The authors also answer a question of A. Stöhr by showing that there is a sequence A of density 0, so that for every basis B A+B has density 1. The methods of the proof are probabilistic.
Classif.:  * 11B05 Topology etc. of sets of numbers
11K99 Probabilistic theory
Citations:  Zbl 202.050(EA)

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